I have also had this issue regularly in 4P human games with items on. We play a small item list, low item team battles and the game has crashed once in each of our (4) 3-4 hour sessions, usually right around 3 hours in. I also don't think it's character dependent, and it definitely doesn't involve any characters just added in 3.0 as none of us play them. It also definitely isn't any of the new costumes because it's always happened in team battles so we never end up using them. I had it happen once in 2.6 as well, but we're OLD Melee players who only just got back together to play Smash a couple months ago so we only played 2.6 once before 3.0 came out.
Usually when it freezes it's mid combat and ends in a freezeframe and digital feedback loop audio noise (weird constant digital horn-like sound). When it happened last Sunday we thought maybe it was because of 4P (it never happens to me when I play solo on the same setup) and we decided to go into Rotation or Tourney mode and play 1v1s. We then literally could not get through the menu entering names and starting a 6-player set before the game would crash again, either freezing with no sound on a menu screen or in the black between 2 screens. At that point, we just tried entering plain VS 1v1s and that crashed after character select but before the match (don't remember if they chose a stage), never coming back from a black screen after something faded out. Then we decided the smash gods deemed it would not be so and we played something else for a while. We'd never tried either mode before so I don't know if that's a regular thing.
Usually after a crash we just started it back up and it's run fine for the next hour or so in 4P teams. I have literally had the game running since they left on Sunday evening. It's been either at title screen, in training mode or in 4P battles with me and 3 CPU for 3 days with no issues. That's always been my experience playing solo (I don't always leave it on 24/7, but I was curious - doesn't seem to be my drive crapping out or something). Now I can setup and play the first few matches of a 6P tourney or rotation no problem.
I run a USB loader specifically for Project M, I found out when I tried to play it for the first time that my Wii wouldn't read my Brawl disc anymore. So I run the Homebrew Full (not Wifi) set. No custom content or stages at all other than Project M itself.