I figured you were fine at this point, I just wanted the question answered in case anyone else sees it and wonders the same thing.

In all the testing I've done, Lizzy is indeed the best or tied the best at everything, something akin to TT in Diddy Kong Racing, though here we don't even have a Drumstick. Speedruns should absolutely include her, there's no reason not to, it just means that if you want WR you're probably going to need to use her.

Good question. We're also not sure on the details. It is known that Iggy does not run well on emulator and will often crash. When I played this on emulator, around 4 years ago, my game worked fine (other than some emu lag) until halfway through world 5. I think I was using Project64, but I don't quite remember. So this means I played Easy Street on Medium on emulator without any problems, so your post just adds to the issue of iggy being a very poorly and inconsistently emulated game.

As far as running this game, honestly getting and N64 and a cart of Iggy is pretty much the only way I know of at the moment. Thankfully both the English and Japanese carts of it are pretty cheap. Otherwise I suppose you could try other emulators, like Mupen, I just don't know how well it's going to do. When looking into the TAS of this game, Iggy is listed as one of the games that says "doesn't emulate properly", so I doubt you'll have much luck there.