-Fix and balance the jungle. (This. Before anything else!)
-Add map-specific itemization options (my votes are for an Immobilize clicky item and a Blink Dagger, along with Aura or single-target ally buff clicky items that are tuned for 3v3 ... call the immobilize clicky something like Root of the Treeline for lore-related goodness ... oh, and implement Gold-Per-Time items that generate gold faster than on SR to compensate for the intended shorter game duration, and have some of them be used in building the TT-specific support/buff clicky items).
-Adjust summoner spell options if necessary.
-Add an aura effect similar to the one from Dominion (but with different effects) if necessary.
-Add Draft Normal and/or Ranked Solo queueing options.
Pretty much what the OP said, I was just bulleting it out and adding my own points too.
In general I feel like lumping TT under the same "classic" ruleset and itemset as SR is a bad move for the health of the map, since it gets in the way of adequately balancing (and increasing the fun factor of) the map for a diverse variety of champion types. I love both SR and Dominion, and I want to love TT too, but I find it difficult to love TT when the map is easily the least balanced of the three while at the same time also having the narrowest set of viable champions.
TT needs some love in order to get the supports and (most of the) AD carries back in there as viable character choices, while also providing itemization options for countering and/or keeping up with the lame wall-jumping escape/re-initiate bullcrap that TT-OP champions like Lee Sin are currently known for. Just think how much a map-specific Immobilize clicky all by itself would change the game, and all the better if further itemization were added to level the playing field better.