I'd be interested.  

[hider=As for those mechanics]
Gone through writing bullet points as I read them, hope that's useful to you. I really hope it's not too negative because the setting intro sounds great.
[list]
[*]That's a lot of hp, if you're doing only 1 damage per turn (and therefore per attacking post) it's going to take a long time to whittle each other down. Even the best case scenario is 5 turns (and that's without missing)
[*]A longer fight wouldn't be bad if it was interesting, but with how simple it is, there's not going to be much variety in tactics. Just not sure how interesting anyone can make doing the same thing 5-10 times in a row sound. 
[*]I'd suggest making the fights shorter by handing out less hp/more damage, fights in the games are usually pretty fast after all. 
[*]You could try for a more complicated system, but I know a few attempts that have been made to turn pokemon into a ttrpg and it's a lot of work and it really doesn't seem necessary for what you've planned, so I'm not about to suggest it.
[*]So with the current system I think toxic would be a bit OP, with how long these fights would take that increasing poison damage would stack up fast, by the third turn it's outdone a super effective same type attack by 50%.  
[*]Similarly, paralysis being a 4/5th chance to not attack seems a bit high and would really drag things out. It's strong already in the games with only a 1/4 chance to stop you acting.  
[*]Sleep might be OK, it'll take far fewer turns away than paralysis, which feels a tad backward, but is more on how crazy an 80% paralysis chance is. It is rather effective, but that's true of the games, I'd suggest doing what they do any making sleep inflicting attacks less accurate, probably just a 50% chance since stats aren't a thing.
[*]Confusion is similar to paralysis, shuts things down way too hard.
[*]Stat influence seems a little unlikely to do anything, but otherwise fine.  
[*]I think you might want to make levelling a little faster, only every 20th level actually does anything in your system and with 3 battles per level that's 60 of them. In general one thing I've seen from other pokemon games, and ttrgps in general is that you probably don't want to actually simulate grinding against random encounters.
[*]Not sure what to say about the contests, sounds pretty close to the games I guess, I've never really paid much attention to those so haven't got much to say, sorry.
[/list]
In general if I had one big suggestion, make a setup that'll make resolving encounters with Gym Leaders and Villains fun, and don't worry too much about the random encounters on routes, closer to what you'd read in a fanfic or see in anime (not that I've actually watched that since gen 4). There's a big difference between running back and forth in some grass pressing the A button and writing out a full description of every turn after waiting for another person to roll some dice. Of course this is subjective.[/hider]