I quite like the Reserve mechanic and permanent Duration cards. If done the right way and with moderation, they give you a mild board presence which adds something, while overturning neither what Dominion is, nor—maybe more importantly—what Dominion isn't.
The famous quote by Antoine de Saint-Exupery springs to mind: "A designer knows [they have] achieved perfection not when there is nothing left to add, but when there is nothing left to take away." — Don't go crazy, show some Reserve-ation, but explore this space a little more.
Of course, phrasing the new batch of Reserve cards is tricky: either you print a second set of Tavern mats, or you don't reference it, or you do and explain in the new rulebook that you can just pretend to have a mat somehow, or... something.
There's already a mechanism for abnormal discard timing, and that's duration. Maybe you could do something like
Duration Coin
Treasure — Duration
Cost: $2
+$1
—
Directly after resolving an Action, you may get +2 Actions if you haven't done so already.
Once you take your +2 actions, Duration Coin has nothing left to do and will be discarded in your next clean-up phase. One difference is that it'll be in play rather than on a mat until you "call" it. It feels rather clunky, but I think it recaptures the reserve mechanic while neither (a) needing a Tavern mat; nor (b) jumping through completely horrendous hoops to avoid needing a Tavern mat.
Idol kinda' reintroduced the journey token, except the set of cards which shared the new journey token is {Idol} and it resets every turn. More of that could probably work fine. Meh, it's a thing you can do, not something that super excites me.
Events are cool, one could easily do more of those.
Replacement starting cards is a cool idea, one could... uh, i dunno. "In games using X, each player adds one Y to their starting deck", that does not sound great. Introduce more Heirlooms and use randomizer draw order to tie-break which ones work and which ones don't. That would introduce the unlikely possibility of having heirloomers without their heirlooms, which is... ok I guess?
TL;DR: Reserve, permanent or long Duration effects, events. Do Adventures again, basically
Edit: Oh, also, I enjoyed the modal cards from Intrigue. That can easily redone, see for example
Wild Hunt