After reading some messages, I've come to a conclusion:
You shouldn't have early access on Itchio. Period. The way the pricing works seems to actively go against what you wanted to do with it.
The ONLY workaround I can think of (Itchio might not like it though, and it's probably more work than it's worth) is for you to create a COMPLETELY NEW PAGE each time you want to release an update in early access on Itch.
So you'd have this page becoming the main one, where the updates come out for free once two weeks have passed. Then you'd create an identical copy of this one for the T2 early access version, price it at $20, and move the V0.46 files from the main page over to the T2 one. A week later, you lower the T2's price to $10 and make it the T1 early access page instead (this would be fine and NOT cause the same problems you're having now). HOWEVER, for V0.47 you'd have to delete the V0.46 page, move the V0.46 files to THIS one, make another identical copy, add the V0.47 files to it, then price that NEW COPY at $20 for a week, then repeat the process with each update.
Now in regards to abandoning Itchio completely... Please don't. Itch makes it fairly easy to find, download, and access these kinds of games. As well as interact with the communities surrounding said games. Abandoning it would most likely result in a loss of visibility more than anything. For me, I'd be more annoyed that I'd have to click an extra 3 times whenever an update comes out. (I'm lazy, shut up)