Help with door hinges

I bought solid core 1 3/4" thick door thinking they would know to put on the proper hinges. As I installed the door, it wasn't closing properly and I discovered that the hinges cannot support the weight of the door. I need to replace the hinges. I would like to be able to have a hinge size where I can screw two of the hinge screws into the jack stud. However, because my walls are 2 layers of 5/8 (1 1/4" drywall), I would need a 5X5 hinge so the door could be flush with the drywall to do this. Since my door is only 1 3/4" thick, the hinge would extend pass the door. I'm not sure how to handle this. I can't seem to find hinges that aren't symmetrical that would extend into the jamb enough to screw into the stud but not extend pass the door.

I would have to see it to really understand what you are saying Tom. But I can say this. A deeper hinge leaf will require more width in the opening for the door to open and close. It seems like a deeper leaf is the way to go in these situations, but it creates a set of issues often not seen until the hinge is in stalled.