Have you been doing GOMAD? How much have you been eating on average?
The big thing w/ the starting strength program as Rippetoe wrote it, is eating enough to gain weight which ensures the linear progression. I would say you are far from ending your novice/beginner gains period, if you can make sure that recovery considerations, specifically nutrition/kcals are taken care of.
Rippetoe recommends resetting when you stall, going back to weights from a number of weeks previous and restarting linearly from there.
I think there is a typical number of 2-3 stall/resets before individuals who follow the program strictly, i.e. do the GOMAD, before they can no longer do the beginner progression and move on to the intermediate phase, i.e. the texas method. A lot of these guys put on 20-30lbs of muscular bodyweight.
4-7 lbs in 12 weeks as a complete novice with a lot of heavy lifting leads me to conclude that you haven't been doing enough work in the kitchen. This may require things such as force feeding, GOMAD, more peanut butter than you care to consume, olive oil shots every hour, grazing on something at all times, etc.
It also isn't meant to be a 12 week program, it is over when you end your novice gains and can no longer add weight to the bar every workout when recovery/food is adequate.
There is really nothing magic about the program, its just the basic core lifts and a lot of food. Another program might be more to your liking, but if you are focused on gaining weight/strength, you just have to eat more.
Personally, I'd reset and give starting strength another go until you stall again as you have made pretty good progress, but really aren't there yet in terms of a strength/bodyweight base.