I thought about this. I tested my HRAP3 (from PlayAsia) and seems fine. But I am not a 100% sure about it. I am going to hook up the second HRAP3 I bought and see if it changes things.
To be honest when I lose about 20 matches in a row I take it out on the joystick :). So I could have caused my own problems.
its probably not the stick’s problem. the stick in an hrap anything is the same thing they use in japanese arcade cabs. when youre doing fireballs i would guess that your problem is youre not hitting the forward direction and the button at the right time. the reason i say this is that you said you were riding the gate edges and it doesnt that that much for the down forward input to register. just make sure you actually hit forward before doing punch, i find that sometimes you get caught up in getting that diagonal input (because the square gate feels like it would have trouble getting it) that you mess up the non diagonal stuff.
imo square gates are a horribly unintuitive design choice made by some japanese guy who thought 4 = 8. or maybe there was a tight budget on corners or something in japan (“no, we can’t make a CIRCLE gate, that has an INFINITE number of corners and will cost a fortune!”). i absolutely hate doing any sort of rekka motion on a japanese stick, when all i have to do on my happ circle gate is down twitch forward YAY MY MOVE CAME OUT. HOWEVER, one thing that square gates are great for is charge characters! with chargers you spend a lot of time doing downback, and the gate has a nice corner there so you can find the direction and charge easily. also dragon punches seem to be easier for me on a square gate since you cant miss the downforward (well you can…but its pretty hard).
for executing stuff with charge chars, i think the first hurdle to overcome is actually charging enough before trying to do the move. if youre having trouble it probably takes longer than you think, so sit on down back some more. another thing is getting used to charging when youre in the middle of doing stuff. for example, bison’s jump roundhouse, low forward, fierce crusher combo requires you to start charging when you jump, otherwise you wont be charged enough when you want to do the crusher.
is it weird that i have never played a shoto in any street fighter, even as a little kid? 
youd think that after all this time i would have at least played some games with ryu or ken, but nope. i can execute their moves just fine but i know much about their gameplan other than throw fireballs and anti air with DP.