Thinking through this right now. We've used FanSoft to run our in-person auction for years now, and the new online version is a lot better than it used to be, but it's still not awesome. In particular there doesn't seem to be a way to display money left/bid remaining for each player, which is kind of the most important part of the auction software.
I would not go anywhere near MFL's software. It sucked back when my league was hosted on MFL years ago and it's frankly shocking that it still looks exactly the same. That company has been totally mailing it in for years.
In my search I found one I hadn't seen before, Drafty (
https://draftysports.com/), which looks like it's pretty well put together but limited in functionality. If it covers your needs it might be a good option.
The major hosting sites all have limitations that don't work for our league because we use decimal prices. (Which is kind of silly but it's a 20+ year history and there's no way it will change now). We could get around it if they would allow the auction budget to be $10,000 (just multiply everything by 100) but they're limited to $1,000 for some silly reason. We also have no interest in having to manage timers.
We're probably going to wind up going with FanDraft, using the in-person version with a human auctioneer and sharing the screen.