Make a new game mode that's good and will get popular then boom done. Until then it will carry on like challenges unfortunately.
Unfortunately, It's not that simple. Just having a popular idea isn't good enough if nobody can emulate it. If you look at the past trends, Deathmines are honestly the most complex that has become big. Before this, We had skilling maps. Which was basically just a map where you stood in a box holding down the trigger for various skills. That took no skill (Heh) to set up and thus became all the rage especially since skills mattered a lot back then.
Before that was challenge maps as you mentioned which literally just required you to place blocks with gaps in them. It didn't mean the map was any good, That's just all that you had to do.
Now that we've looked into the past, Let's look to deathmines. They have at least a few orders of magnitude more complexity to them than any of these previous trends just by their nature. You need to have refill scripts for all the mines, In most of them, You need to query a player's avatar so that you can make skin mines, A good portion that I have seen also have scripted shops and ATMs. And there's even more complexity in the higher quality ones. Do the hosts generally know how the scripts they use work? Probably not. But the knowledge required to set up even a terrible deathmine is far more than any of the previous trends.
In order to set up a trend to surpass deathmines, I think you would need to have a few elements.
1: It has to be fun to a large group of people.
2: It has to be something that cannot already be incorporated into someone's deathmine.
3: It has to be more complex than deathmines, But not complex enough that people will be unable to recreate it.
4: It has to be easy to make. Not just in terms of the complexity, But the time it takes to make it. The reason you don't see loads of RPGs is because the process of building the world, And the process of designing a story is extremely time consuming.
Using these criteria, I feel that if TM360 were to hypothetically continue on with large amounts of players then the two top contenders for a new trend would either be scripted PVP deathmatches (As in actual deathmatches.) or minigame maps.
Deathmatches have the bonus of attracting the already existing deathmine crowd whilst being extremely easy to set up and being fun with complexity.
Minigame maps fall into the same idea here. They are really easy to set up if you put a little more effort into it, They are fun and offer a great deal of complexity. In addition, Every map can be unique.
These statements are also based on my world browsing where I have seen a decent amount of both to contrast the deathmines.