Far less than infinity

Gloomhaven scaling has some issues.  At level 1 you are supposed to fight level 1 monsters, and that is an appropriate challenge.  At level 9 you are supposed to fight level 5 monsters, and that is not an appropriate challenge.  You crush them, it is easy.  You are supposed to address this issue by raising the difficulty of the monsters, but there are two problems with this.  The first is that monster difficulty caps at 7, and that isn't enough for really good groups, and the second is that the ways the monsters scale doesn't work.

Monster scaling mostly just adds health, damage, and speed.  Monsters do get additional bonuses like Immobilize or Poison on their attacks but that isn't a huge deal.  The real issue is that, as one person said in the comments on my last gloomhaven post, if you increased monster damage to infinity that wouldn't actually be a huge problem a lot of the time.  You don't deal with high level monsters by having a lot of shields and health.  You deal with them by disarming them, stunning them, or killing them outright.  Their damage scaling doesn't matter at that point, and when you use instant death attacks their health totals don't even matter!  Nothing about monster scaling prevents you executing them, and that is a problem.

High level abilities and equipment let you spew out status conditions like crazy and lock up the monsters until they die.  This is a problem in all kinds of fantasy games like DnD or WOW - just look at the way that designers give special baddies ways to cheat on saving throws against Hold Person or Polymorph.  They know that those effects are absurd in some situations.  WOW had a variety of systems preventing people from using chained up stuns on enemies, for example, because they didn't want enemies to just be stunned for eternity.  At low level where status conditions are rare this isn't an issue, but eventually they become so plentiful it becomes a problem.  At low levels disarm prevents 2 damage, and heals restore 3 health.  At high levels disarms prevent 5 damage, and heals restore 5 health... but disarms get handed out on big AOEs, and heals are tightly regulated.

So you can't just scale monster difficulty by giving them more health and damage.  That just makes healing and tanking even more pointless, and makes instant kills and status effects even better than they are.

What to do?

The answer is that you have to nerf players.  Players don't like this, but sometimes it is necessary for the game to work.  Gloomhaven, like many other games of its type, works best when you get hit and heal up, not when you never let the enemies have a turn.  Complicated formulas like WOW's diminishing returns on status effects are not possible in this format, but we can make other changes.

There are two ways to approach it, I think.  The first is to deal with the effects that are overpowered at high difficulties - status effects and instant death.  Instant death is easy to deal with.  Any effect that instant kills a regular monster does 8 instead.  Still strong compared to regular damage abilities, but not capable of dealing 30 damage to monsters.  It forces you to respect their health totals.  Instant kills that kill elites do 12.  Again, big numbers, but not that far out of the realm of what beatdown can do.  Curses don't delete an enemy attack entirely - they count as -3.  Still excellent, but big hitters still get to punch.  You can do the same for disarm.  At low levels these still function basically the same way, but at high level you don't get to just ignore the enemies.  If you really want to tear off the security blanket, then make curses and disarm only impose -2.

That deals with some of the problems.  The other problem is that gear combinations get out of control, and this is largely to do with stamina potions and the fact that players get so many potion slots.  Deleting stamina potions entirely prevents people from running outrageous combos back to back, and that goes a long way.  The other choice is to simply say that you get 1 potion no matter what your level is.  This basically means that every character takes a stamina potion, which is boring, but it does ratchet back their power level a TON.  You won't have a healing potion if you happen to get bashed, and you won't have other free stuns, bonus damage, and other effects that potions can bring.

In my home game the first thing I would try is nerfing disarms / curses / instant death effects, and combine it with getting rid of stamina potions.  I think that those things combined would leave players with a sense of progression as they accumulated gear but would prevent the worst combos from getting out of hand - you only get one shot at each card each time through your deck, and the most powerful cards that ignore enemy stats don't work.  I also think it would introduce more variety into potion selection because without stamina potions as the high level default choice you have all kinds of interesting stuff to choose from.

Ultimately you don't have to do this - you can just revel in your power when you are high level and roflstomp the monsters all day.  But I loved it when the scenarios were hard and we came down to the last card, and I want that feeling again.  Pulling back on the most brutal of abilities seems like a really good place to start doing that.