In my experience, it's easier to save time in memo rather than execution. So if you're mostly making mistakes in execution, you could try memorizing faster. My goal every attempt is to memorize quickly and then review frequently. So I don't dwell too long on one cube if it's really difficult to memorize since I'll be coming back to it several times.
As for how many cubes you can do, at this point I think it's hard to say. My only 3/3 was 17:42 in April of last year, and now I'm attempting upwards of 13. I'm not world class, but in my opinion until you hit the hour time limit you're only really limited by how much information you can memorize. From there then speed really becomes more relevant. If I had to guess, I'd say ten doesn't seem all that far-fetched.