The 2 shot transition between DA and SA, no ifs ands or buts, is harder to do accurately than 2 fast shots with a DAO or SAO. I don't care who you are, it'll take more time to get good at.
You are in the same predicament, to the T, that I was in 2010. My suggestion is that you do what I did. Take a small DAO handgun, such as a Kel Tec, or a revolver to the range. Grip it with one hand, so hard that your arm starts shaking. Back off by 10 percent so your arm stables. Point it at your target, disregard the sights, instead pointing it at your target. Now, at a distance of 6-12 feet, blast away as fast as you can. This is the basis for up close Applegate Fairbairn Sykes shooting, and in my experience the easiest way to shoot micro mouse guns. It may take you 100 or 200 rounds, but you'll get good at it.
DAO mouse guns are simply not well suited for sight picture use. They're too small, and too snappy with too long of trigger pulls to be shot at ranges beyond that which point shooting is capable. Yes, you can take your time, stage the trigger, and shoot more accurate long range shots. Good luck shooting a micro .380 DAO with that much precision at any distance at a combat speed. That's why I agree, I'd rather have a DA/SA and have the long range capability of a gun like a P238. But it doesn't exist just yet.
The good news is that once/if you come to terms with these current facts of life, the Seecamp and copycat models are much smaller than the guns you're talking about, in fact being the smallest on the market without going down to .22 or .25, have okay DAO triggers, and with practice and ball ammo are capable weapons out to 15 feet or so. And that's further than the majority of concealed carriers could ever expect to have to have to shoot from in a defensive situation.
If you go larger, such as up to a 380 Kel Tec or better yet the Kahr, you'll have much more accuracy potential. Go for the PPK sized Taurus, and you'll be formidably armed with a shootable platform with a good deal of power.
It's all a trade off going up and down. You just have to decide what fits your needs. The bottom line is this, trust me, you can get good with whatever you need to. It just takes a desire to do it.