Please note this is my 2 cents.
When i shoot 6/ 10 pin spares i use the same ball i use for regular bowling. I, like you scoot left of center to pick these leaves up. my biggest problem I found, is that when I'm trying to pick up these pins from that angle, I tend to open my shoulders back towards the pin, which in turn makes me miss the pin to the right mostly. I really had to work at keeping my foot straight to the foul line , and not turning my body towards the pin to try and pick it up. when I was able to start doing this my carry percentage when way up on spares on the right side. this may not be your problem, but I have noticed it from quite a few people at our center that have problems picking up those certain corner pins.
I do understand that missing to the right was not in your post, however the idea of turning your shoulders towards the pin would make you inconsistent enough to miss either to the right or left, as it is hard to consistently turn your shoulders or foot, at the proper angle