An AI Progress of 400 is not horrible at all, I tend to have 400-500 when going for the final AI planets. Be aware: when you destroy the first AI home planet, you're going to skyrocket by 100 AIP. So, if you can coordinate attacks that is nice, but often that is not possible -- definitely sounds out of the question in your case. If you've taken that many planets and have that low of AIP, you've done a very good job of striking data centers, which is great.
The final assault is difficult, moreso than any one Mark IV planet, but here's the thing: if you keep the AI from noticing you, it can be very easy, depending. It's all about how you alert the AI and when, and what the AIP is when you get there, and how well you are able to reinforce.
I don't think I've ever managed to take out an AI home planet with just one wave of ships, in solo or multiplayer, so be prepared to take multiple runs. Since all of the ships on the planet will come after you when you are attacking the home planet command station, that means you'll want to make your first priority to destroy all the guard posts. Then getting rid of any force fields and/or fortresses. And lastly, taking down the command station itself. Try to do that when there are as few AI ships remaining on the planet as possible (within reason), since those ships will come after your own planets when you destroy their home station -- I've literally lost, just when I thought I was near to winning, in that fashion.
Once you are certain you are safe from a counterattack (keep an eye on Threat), then move your ships and your production facilities over to that second planet, as you were thinking. Just don't expect for any one strike group of yours to take out the entire enemy home planet at once unless you are really lucky and they are caught really off-guard.
That's the other thing: assuming that the home planets are not on alert, hopefully they only have a few hundred units there. Even so, that will quickly grow to maybe a thousand in a short amount of time once you tip them off, if you are not constantly whittling them down there. If you keep them on alert for any extended period of time, you make your job exponentially harder as they will quickly climb up toward 4000 or 5000 ships there.
Anyway, so lightning-fast strikes against the guard posts, with new waves coming immediately after your first ones are destroyed to fill in the ranks, should do it. It might turn out to be a really easy encounter for you if you've taken so many planets on the map and have so many ships built up, etc. On the other hand, it might not. Be prepared for the worst, and if you get lucky -- great. But still be prepared for the worst when you then approach that second AI home planet, too.