I think it's fairly do-able, as long as you don't mind lots of walking.
My kids and I did 3 of the parks on President's Day Saturday. That wasn't our goal going in, but that's how it worked out.
We got to AK at opening and walked right onto EE. (AK opened at 8:00 that morning). I had planned on spending some time there, but the kids decided they'd rather go to EPCOT. So we drove over there and got in just at FW's opening (9:00). We pulled TT fast passes, did Soarin standby (about 30 minutes wait), pulled MS fast passes, rode TT then used our MS FPs. It was probably 11:30 by that time. We then walked back to Japan and had lunch at Yakitori House followed by some time in the big store.
DD then decided since she was that close, she needed a TOT fix. So we walked down to MGM (stopped at Beaches and Cream for ice cream on the way), and she did standby on ToT while I pulled RnR fast passes. We did the animation tour, and WWTBAM as well, and watched Fantasmic before walking back to EPCOT and driving home. We were on I-4 by 8:30.
Since you would only be interested in the big rides, I would think that in the time we spent doing Japan and the other non-thrill rides at MGM, you could go over to MK and do the mountains. I've always found that fastpasses at MK are more available than EPCOT or AK, since there are many more fastpass attractions at MK.
I will tell you that I was ONE TIRED PUPPY the next day. I estimated that I walked about 12-15 miles that day. But you could do less if you took the boat from EPCOT to MGM, then the bus over to MK from there.
Hope you have a good time!