When I say three stats, it should be pointed out that there are in fact five stats that routinely come up (plus WOUNDS, which I almost think should be rolled into LUCKY somehow). As to the matrix, I would suggest something like:
When you . . .
assault an enemy position . . .
lead by example . . .
keep it together under pressure . . .
perform a combat action requiring bravery, steel, or resolve . . .
roll GUTS.
When you . . .
provide covering fire for your team . . .
give orders . . .
pause for a moment to assess the situation . . .
camouflage or hide something . . .
perform a combat action requiring intelligence or logical thinking . . .
roll TACTICS.
When you . . .
take cover under fire . . .
scrounge for supplies . . .
perform a combat action requiring luck or where the critical portion is out of your control . . .
roll LUCKY.
When you . . .
start a new engagement . . .
have a (not otherwise unwilling) NPC take an action on your behalf or under your direction . . .
perform a combat action which is carried out by NPC soldiers. . .
roll OP.
When you . . .
petition up the chain of command . . .
spend time improving your bond with someone . . .
barter for goods or services . . .
roll SMOKES spent.
I think three stats evens out and clarifies what each are used for without meaningfully reducing flavor. I think 'collapsing the range of playbook differentiation' is the wrong way to look at it, as the unique moves are what most meaningfully distinguishes playbooks--if a high stat distinguishes all the actions a character does in his role, there is little point of having multiple stats to begin with.