Besides the rewards you already mentioned, there is a bonus for every raid you win that is based on what league you're in. It's usually small, but it can make a difference.
There's also the same reason there are leaderboards in any game - to see how you stack up against other players!
There is a downside to having many trophies, and that's that trophy count is an important factor in matchmaking. Thus, if you have many trophies you're going to get raided often by high level players, and you're likely to get matched up against hard opponents.
Many players that I've seen will try to maintain or lower their trophy count in order to find easier players to raid. You've probably seen players dropping trophies in this manner - usually, they will deploy a single troop against you, or they'll put out and immediate recall their hero units.
I'm in a similar situation (albeit at TH7). I've got half my walls yet to upgrade, which is going to cost many millions in gold. However, I just finished my last lab upgrade and don't have that much left to spend massive amounts of elixir on.
You've touched on higher cost raids in your question. It is true that BAM/BARCH is a solid strategy, but it is very low cost in terms of elixir.
Right now you might want to focus on dark elixir and gold, so you may want to completely trash bigger, better defended bases for maximum loot. Dragons take a crazy long time to train, but you might consider Giant/Healer or perhaps Balloonian raids to give you a bit more destructive potential and use up some of that elixir.
Having a whole bunch of elixir in your storages deep inside your base is a good way to get raided and completely trashed. This is going to cost you gold and dark elixir, which is a bad thing.
Right now I've got my elixir storages outside of my walls, and I like that pretty well. I've trapped them heavily, to get people to commit a lot of their troops to taking them down. This tends to end with me earning trophies from them at a cost of elixir. This has two benefits:
- Gaining trophies, which will give you bigger fish to fry when raiding and let you occasionally take resources from bases without getting a star
- Give you "sucker bases" to revenge when you're online. Revenge is a powerful tool for finding bases where you can take your time, plan out a strategy, and take their stuff.
I wouldn't suggest preemptively upgrading your town hall unless you're sure you're ready for it. Some of my clanmates have moved up early and found that the resource penalty causes them major issues. This lengthens the time it takes to get enough resources together to make your upgrades.
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For me, I got to about 2300 trophies just by town hall sniping!