Go the initiative route. If you really want to make it closer to a time based system, check out what Alpha Omega did.
I thought there was another chart for this, but I guess not.
The part we're interested here is the leftmost column (stat) and right most column (active segments).
Basically, as your reaction went up, you acted more often. Shooting a gun or swinging a sword took your whole action (and you'd act again in your next active segment). Casting spells took up a certain number of
seconds (each segment is 1 second), so if a mage had a reaction of 16, they act in segment 3 and cast a spell, taking 4 seconds to cast. In segment 1 the spell would complete and take effect and the mage would get his next turn (in segment 1). If he instead cast a spell that took 1 second to cast it'd complete in segment 4, but he couldn't act again until segment 6.
Large bore weapons (mortars, etc) took a certain number of complex actions to reload. So a guy with a 16 could reload a mortar in 12 seconds, whereas a guy with a reaction of 22 could do it in 8 (but would end up waiting for his 10 reaction companion to fire the damn thing 4 seconds later).
This route might be too complex for your needs, but it's a hybrid of the two systems.
The Dice Pools thing you see here is confusing, but I'll give it a once over. Before segment 1 (and after segment 6) your dice pool of 6 dice refreshes to full (or possibly less than 6 dice, if the stat is below 12). You only get these 6 dice over your entire turn, so if you have 100 reaction and 6 active segments, and want to make an attack in each, you only get 1 die to do it. The upside is, you always take your largest dice first. So if you have a 26 in agility (for firing guns) you get 1d8,5d6. You take 1 die from your pool in segment 1: 1d8. 1 die again in segment 2: 1d8. 1 die in segment 3: 1d8....
Or you take 3 dice then in segment 4: 1d8+2d6, and stand around segments 5 and 6 doing "non-dice" actions (talking, moving, etc).