...you can't typically fire for both of your simple actions...
No, but you can fire for a full complex action (which would be shooting for an entire action phase)

(With FA that would be 10 bullets. With BF that would be a Long Burst of 3+3=6 bullets. With SA that would be a SA-burst of 1+1+1=3 bullets).
In this case you would not reset recoil between action phases and you would get progressive recoil that carry over (no matter how you read the rules).
If you only spend a simple action (only shooting for half an action phase and with your other simple action taking an action other shooting -- or "not shooting for an entire action phase") then you would reset recoil until the next action phase(*)
(With FA that would be 6 bullets. With BF that would be one 3 bullet burst. With SA that would be 1 bullet. With SS that would be 1 bullet)
(*)Depending on your interpretation of RAW. As I said, there are two ways to read the rule.
Personally I think it make a lot of sense that if you take time stabilize your weapon between your bursts (only spending a simple action to fire bullets) then you would not get progressive recoil the next action phase. If not then you run into the dilemma where you can have a marksman expert strength maxed out troll with a gasvent 3 light pistol in a gyromount (for sake of argument we bend the rules and let you use a gasvent III and gyromount on a lightpistol) shooting one single bullet every action phase (which is once every 3 seconds or in some rare cases once every 1.5 seconds for most non-wired trolls) eventually getting so much recoil that he can not hit a stationary unaware target 2 meters in front of him. That simply does not make sense.
At my table recoil reset to zero if you spend a simple action not shooting bullets. At this point I don't even think I have to call it a house rule (this is after all the interpretation that Aaron did as well. I read no indication from any other official freelancer or official developer that it would work in any other way).
If you want to use progressive recoil between action phases when you only fire one single bullet or one single 3-bullet burst (and more importantly if you think it make sense). Go ahead. It is your table. Your rules.