Ohm is Futile

It's possible, but hardly necessary. That said, if you want three (note: you could use two and use Kerbin as your third "relay") satellites in orbit around the sun, the easiest way to do it is to use some form of tool like KER to tell you your orbital period around the sun. What you do is launch your three relays and drop their orbital periods down to two thirds of Kerbin's orbital period: 284 days. This is best accomplished by doing an escape burn from Kerbin at dawn. The rest is fine-tuning your orbit until whatever tool or calculation you've made confirms that your satellites are on an orbit around the sun that takes 284 days. (You could always look in-game at your time left to apoapsis just after passing it, if it says roughly 284 days, then you've done it successfully)
Once you've done that, you need to circularize one satellite's orbit back to 426 days at apoapsis. Assuming you leave one satellite on the same orbit as Kerbin or use Kerbin itself as a relay, it should take at most two orbits or 568 days until you have a perfect triangle of relays around the sun.
That said, you don't really need to worry so much about the sun eclipsing your network. Assuming you place an interplanetary relay near each planet you are going to visit, you should have plenty of hops to get around the sun without a network dedicated to that.
EDIT: My approach to interplanetary relays is to put a relay with RA-100s on the trail of every planet I plan on visiting and use a local network with satellites equipped with a couple of RA-2s to avoid interruptions from local satellites.(I mean natural satellites here, like the Mun or Ike, etc.) The easiest way to achieve this is similar to what I mentioned above: you perform a fly-by or do an escape burn at dawn that leaves you on a smaller orbit than the target celestial body. Soon after that, you burn radially to match that celestial body's height around the sun and prograde to match its orbital period. (you probably want a longer orbital period by a margin of a few seconds to avoid catching up to the planet and falling inside its SOI) This leaves you with a strong signal that always comes from that planet's trail and is at virtually no risk of being eclipsed locally. With 2 or 3 of those bouncing signal around different planets, there is virtually no chance to be eclipsed by the sun.
You could always not bother with that and just build all your local relays with RA-100s, it's just less efficient in terms of money, but you did mention it was a sandbox save.