What bewing said about splitting your burn over 2 orbits. That'll knock time off the longer, trickier burn.
For the 2nd burn, I'm going to espouse heresy: Ignore what the transfer-window planner tells you for all except the day (ish) of departure. Your high-efficiency, low-thrust transfer stage will not be able to make the desired burn with sufficient precision.
I've had success getting to Eeloo and Dres with the following (and my apologies in advance for the Giant Wall O' Text):
1) Set up a "dummy node" from LKO with a prograde burn that gives you an Ap at about the right distance from the Sun and an ejection from Kerbin SOI that's parallel/tangent to Kerbin's orbit. That tells you where you need your FIRST burn in order to get its Pe in the right place. (You won't get an encounter; you likely won't even get 'closest approach' markers. Don't sweat it. Just rotate map view so you're looking "down" on the whole solar system and eyeball it.)
2) Reduce the magnitude of that burn to give you the first burn that bewing mentioned. (I'd recommend setting this up for a day or two before the optimum launch day, and a dV of around 800-850 m/s; this will put you a bit late for the optimum launch window, but that shouldn't be critical--Eeloo wants precision in the trajectory burn vs trajectory planning, but it doesn't need to-the-hour precision timing for departure in my experience).
Once you've made that burn, set up your transfer:
3) Repeat Step 1; this node should be ~800-850 m/s smaller (and correspondingly shorter duration) than what you had in Step 1 in order to achieve a similar trajectory. Again, you won't get an encounter; don't sweat it.
4) Drop a node onto the transfer orbit (the simpler and more reliable method is to put is on the ascending/descending node, but it's often more fuel-efficient to put it earlier. That's REALLY fussy, though, and I don't recommend it if you've got enough dV--especially for your first time). Set up a plane change to bring your intercept point up/down as needed to get closer to an encounter. Your goal here is to get a "closest approach" indicator.
5) Once you've got that, fuss with BOTH of the nodes from steps 3 and 4 (the "plane change" node will likely need some prograde/retrograde and radial components), driving the closest-approach distance ever smaller until you get an encounter,and then focus view on Eeloo and use the same technique to drive Pe smaller. (This last part should be familiar to you from fine-tuning arrivals at easier planets.) Ideally, try to achieve a collision course so as to have the most room for error later, but don't get TOO fussy about it.
6) Once those 2 burns are arranged to your satisfaction, prepare to execute the Kerbin-escape burn. In map view, get the plane-change node from Step 4 as near the "camera" as you can reasonably manage--you'll be watching it like a hawk for the last 100 m/s or so.
7) Execute the Kerbin escape. For a long-duration, low-acceleration burn like you're going to be doing, I kind of 'split the difference" between burning prograde and burning to the node: I'll burn basically prograde, offset about 10-15 degrees in the direction of the node. You'll need to adjust your pointing over time, and you'll eventually shift from burning somewhat radial-in to somewhat radial-out.
8) As you get down to the last minute or so of the burn, shift to a basic prograde burn and go to map view (if you aren't already there) where you preset your view for the plane-change burn in Step 6. Your goal is to place your actual trajectory right smack on top of the planned trajectory at that node. IGNORE WHAT THE NAVBALL SAYS ABOUT HOW MUCH BURN YOU HAVE LEFT--you want to match the TRAJECTORY, and that low-accel means you won't exactly match the dV of KSP's "instantaneous-velocity change" node planning model. Cut engines when you're as close to nailing the trajectory as you can manage--rotate ship and make a short retrograde burn if you overshoot. (I am also shameless about knocking the thrust limiter down to 0.5% for tiny final adjustments; it's cheaty, but OTOH the stock game doesn't provide any REALLY low-thrust maneuver/attitude jets, so I justify it that way.) Once you've managed that, delete the Kerbin-escape node.
KSP will now lay your planned midcourse node onto your ACTUAL transfer trajectory rather than the initially-planned transfer--on a trip as long as Eeloo, there WILL be errors. That's okay.
9) In map view, focus view on your destination (Eeloo). See how close you got. If you're very lucky, you may still have an encounter. Even if you don't, you've probably at least got closest-approach markers, and should be able to adjust your midcourse burn to regain the encounter and place your Pe where you want it.
10) When it's time for your midcourse plane change, focus map view on Eeloo and watch THAT for the last 100 m/sec (-ish) of the burn, with the goal of eyeballing the last bit of the burn so you match the planned trajectory as best you can. Again, that's more important than precisely matching the planned burn time/dV.
That should get you there. It's not a technique for the impatient, as there's a LOT of fussing about re-fine-tuning nodes that you've already fine-tuned once before. But Eeloo isn't MEANT to be easy.
Let us know how it comes out!
Ah-ha! As SO OFTEN happens when I admit publicly that I can't solve a seemingly-simple problem, IMMEDIATELY after posting the question I sorted out an answer that worked at least for me. Posting here in case someone else has a similar issue and wants a similar solution.
My desired parameters: delete the files I want deleted, while retaining the ability to use Steam's sync to cloud feature in the future--see above re being glad of this feature if my files actually WERE corrupted. (So turning off cloud sync in Steam won't work for me, since it retains all those old saves and will 'restore' them the moment I turn the feature on again.)
The solution that worked for me:
Start KSP
Go to Settings and run in window rather than full screen
WITH KSP STILL RUNNING:
Go to Windows, bring up my save folder overstuffed with old saves
Mass-delete old saves as desired
(Optional) Go back to Settings and revert back to full-screen mode
Quit out of KSP
Steam will re-sync its cloud files when KSP starts and again when it quits--but if done as above, it ends up syncing that folder to its state AFTER DELETING all those old saves.
I'll have to go in and do this again every now and then, but it lets me keep the useful parts of Steam's cloud-sync while still letting me declutter my saves.
Why do the big tanks need bigger docking ports? (Serious question--I'm not an RO player, and there may be subtleties either in RO/RSS or in your use case which I'm unaware of.)
If it's just for structural stiffness (which seems to be the most common reason for wanting bigger docking ports), there are other ways to get that.
The brute force method, of course, would be the Kerbal Joint Reinforcement mod, but that affects all joints everywhere and is not to everybody's taste.
For a more focused solution (though it does increase part count), Kerbal Attachment System has EVA-deployable struts which are designed specifically to add structural strength/stiffness across docked joints. And I believe there are other mods that offer similar strut-based solutions.
You can also increase docked strength with no additional mods by using multiple smaller ports instead of one big one (again, at some cost in part count--and you have to be GOOD at aligning craft properly when docking).
Not in keeping with the spirit of RO, but probably still doable unless RO changes the dimensions of rocket plume heat/damage effects: you can dodge the issue by using a "puller" design rather than a "pusher". Sure, the overall craft may still resemble overcooked spaghetti, but it's a lot easier to pull a noodle than to push it.
I'm sure there are other solutions out there, but those all came to mind immediately.