So... I had a thought in the shower last night but I won't get chance to test it until tomorrow.
If you launched precisely 2 years ahead of your transfer window to Jool/Eeloo/modded-outer-planet, and put yourself on a solar orbit with exactly 2 years period, you should re-encounter Kerbin again at the time you should be launching. Moreover, you will be tangential to Kerbin's orbit, just like you would be when launching out of LKO.
Does this actually produce a gravity slingshot, or do you end up doing a flyby at LKO altitude at exactly the same speed you originally left it? My tiny mind cannot seem to grasp this one
(I'm playing with OPM and Kerbol Plus Remade, so the distance to the outer solar system is considerable and I'm looking for any advantages I can gain to get low-tech probes out there, but ad-hoc flyby planning tools don't seem to exist.)