Do these exist outside of the WSOP? I could see people being interested at my local poker room, but the tournaments are always the NL variety.

My local room has them once or twice a year.

LHE is way less popular than NL and even NL tournaments are struggling.

If you want to try and start one, I'd suggest making a one time event first. Talk is cheap - way more people will say they're interested than will show up.

LAPC at Commerce in February has a decent amount of limit and mix tourneys. There’s usually 3 stake levels for these: $350, $570, and $1100s

The $1100 drew a decent amount of players and had one re entry, many of whom are firing away at variants they aren’t great at, prob bc there is like $50/60k leaderboards for best nlhe, best non-nlh, and best overall leaderboard. I played two tourneys (chopped the lhe 3 ways) and some ok cash games and snuck into the money for the non-nlh leaderboard but had to leave town before I got my $48 and prob forfeited it by now

Other than that, I think one of the MD casinos tried one, but haven’t heard of them running it again. Not a ton of interest in lhe tourneys overall