Sorry in advance for the TL;DR post. Hopefully it's useful to someone. The most useful bit is in italics and is credit "Sir Georgeous Games" on youtube. He shows it working with bb-8 in the ABC squad for heroic tank.
Thrawn will definitely have to attack with his basic at least once between each use of fracture. It's unavoidable because of the cool down on fracture and GAC (both are 3 turns with omega).
There is an interesting RNG dependent way you could get two fractures off quickly based around the team and turn order the OP suggested. But its down to turn meter gain for FO under KRU when a FO crits. So, Thrawn fractures, FOO gives marching orders, GAC to FOO, Pinning shot, Kylo lashout. Now comes the RNG prayers. If you got crit with FOO he will get some TM and after thrawn's basic can give marching orders to Thrawn again who fractures. If you are insanely lucky maybe that would give you two fractures before too many turns from the other team but doesn't seem reliable (I haven't tired it).
Maybe the better TM manipulation tactic with thrawn and FO is aimed at getting fracture back as soon as possible when it expires naturally. Use thrawn's basic as he comes out of fracture, Give TM back to thrawn (with FOO in this team) and immediately turn meter swap with whichever character has the most turn meter and you'll have fracture reapplied ultra fast.
I'm no expert but like the OP said FO can do well even in very competitive shards so long as you accept a long climb every day. The generally recommended tactics for FO from the people on the FO discord that use them effectively in arena is that the core team seems to be zKRU/FOO/zFOST with either FOX or FOTP in one slot and Kylo or FOSFTP or Thrawn in the other. It's a bit in flux though because of more people getting FOX.
The tactics are also really simple... farm lots and lots and lots of mods and eventually your FOO will be at a point where it's going first. Then give marching orders to FOST and you get your taunt up and all of your team gets turn meter so everyone goes once before the other team. Then control dangerous characters with your stuns and wait for all of that lovely health and prot regeneration from the current AOE debuff meta.
