Speed doesnt come from being fast, it comes from being practiced and smooth.
People who worry about the trigger on DA gun are actually worrying about the wrong thing. They should be worrying about the sights, and keeping that alignment, while stroking the trigger. By stroking the trigger, I mean pulling all the way through, without hesitation. Staging the trigger is just the DA version of a SA trigger, and really not the proper way to shoot them.
Lightening doesnt necessarily make the trigger better either, although many seem to think its important. Most DA autos and revolvers have decent DA trigger, and some are downright nice, even if they are not "light".
Dry firing is one of your best bets here. If you practice focusing on your sights while you stroke the trigger, and concentrate on keeping the proper sight picture through the whole thing, you will start to get the rhythm down and you will see your groups start to shrink at the range with live ammo. By focusing on your sights, and paying less attenton to the trigger, you get two benefits. One, your sights are aligned and on target, and you get a surprise trigger break, which is something you tend not to really get with a single action trigger.
I learned to shoot DA on heavily recoiling revolvers. My SA groups were suffering, especially the more I shot and the more I thought about it. A friend suggested shooting DA, for the two reasons above, and a short time later, my groups started to shrink, and the difference was pretty dramatic. Once I got used to shooting that way, I never went back to thumb cocking them.
I have a number of DA and DAO pistols, and when you compare my single shot DA groups to my SA groups, you'll find the DA groups are usually smaller.
I think once you practice a little while, and start to see improvement, you'll find that your less sensitive to triggers in general, and find you worry less about them. You dont need to spend extra money on them.