Currently I use what is, as far as I know, the typical Tour route for a Fed. Go to Beta Ursae, change instances to teleport to the other side, go through Orellius Block to Eta Eridani, switch instances there again to get halfway, go to Gamma Orionis via the Omega Leonis transwarp, then straight through the middle of Gamma Orionis to Pelia Sector, transwarp to Sol and start over. 200k EC, nice and easy.
The issue is that my Odyssey with Borg Engines, DI+RP, no Driver Coil at all, and a Very Rare Astrometrics Doff I still have to wait about 25 seconds at the end of each run waiting for transwarp to finish cooling down. Despite this I can squeeze in 10 runs before Tour is over, but I've seen some people say they have 9 in Driver Coil with a similar setup and can get far above that, even some claims of 3 million EC (possibly a Vesta instead of an Odyssey, not sure which is a better Tour runner). Doesn't seem possible to me without an alternate route because of Transwarp cooldown issue I'm already experiencing.
That route typically abuses the first federation mission as a return point while Transwarp is on cooldown. If you have it in your quest log, you can click it and return to the Azura for some energy credits.. Hit reverse for a few seconds and you're at Sol.
That said, I haven't run tour in quite a while - don't really have the EC problem to require it anymore.
Yeah, that's what I do when transwarp is on cooldown, but getting from there to Sol feels like it takes about as long as just waiting the 20 seconds for transwarp to finish. Haven't tried going in reverse from it though, always turned around and went forward to get back. I was just hoping there was a route where I didn't need to abuse that mission, because the pop-up from it is annoying as hell.