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1. Dragging super minions to fountain/turtling - decrease the tower attack range, make minions lose aggro as they approach the fountain.
2. Jungle - Normalize the monster locations in the jungle for a fair game every time. Jungling in TT would suddenly be a viable strategy.
3. Tryndamere - Draft pick mode in normals
4. More ranked exposure - Solo queue
5. Itemization - Gradual experimentation; tweak existing items to have unique TT effects to make the game more exciting.
6. I would also suggest a tiny increase to the speed at which players accumulate gold to give it a more consistently fast-paced vibe.
These fixes are all fairly simple to implement and pretty straightforward. So why not give them a shot? If some or all of the changes don't work out, then roll it back and try something else, but I think this is a solid way to address TT's problems.