The Mini-Jacker is fixed at 4" setback. Other than that, I am basing everything else on assumptions, so I am going to ask a series of apparently condescending questions. That is not my intent, but I need to know my assumptions are correct. A pic from the side of your hull while floating and a pic from the side of your stern/motor/Mini-Jacker taken level with the bottom of the boat with the motor in operating position while on the trailer would be helpful.
1.) You have a standard shaft motor (the cavitation plate is roughly 15" below the top of whatever surface the motor is clamped to). True or false?
2.) You have a standard Gheenoe 15" transom. True or false?
3.) Your cavitation plate is currently level with the bottom of the boat. True or false?
4.) If all the above are true, the top of the clamping board of the Mini-Jacker should be level with the top of the transom. True or false?
5.) Your motor blows out if you move the Mini-Jacker up the transom 1 bolt hole. You've already said this is true, but I want to clarify you are adjusting the Mini-Jacker up the transom and not the pin that adjusts the trim of the motor.
6.) The top of the cowling is roughly parallel with the surface of the water while on plane. True or false?
7.) If any are false, please elaborate.
If all the above are true, you will need more setback to run shallower. You could get creative and shim what you have using 1" aluminum stock. This has my vote since you already own it. You also could look into other options like the Bob's Mini Jack. It will get you a max of 6 1/8" setback for 12# of weight. The CMC T&T will get you 5 1/2" setback for 24# of weight.
However, you can't get too crazy with setback without moving the COG aft, squatting down the stern and decreasing resting draft, which is more important to me than running draft. Tuning a motor/hull combo for shallow running is a balancing act specific to your boat. Regarding the CMC T&T, I wouldn't want to add 24# to the back of a 13 footer with a tiller motor, but since your motor is pretty light you could make it happen if you move your batteries and fuel forward.
A trim and tilt will not get you shallower by itself. It will help you get on plane quicker and maintain perfect trim at slower speeds regardless of the balance of the boat. With small boats that are balanced so they float level, you don't need one as much, but they are definitely nice to have.
The setback is what allows shallow running because it allows the motor to be mounted higher to take advantage of the hump of water which wells up behind the hull at speed. As a result, the cavitation plate is higher than the bottom of the hull. T&Ts are frequently confused with hydraulic jack plates, which are a whole other creature. The super sexy flats boats that run in inches usually have tunnels, T&Ts, hydraulic jack plates and power trim tabs. They also have the size and speed necessary to make the system work and keep all that heavy shtuff afloat.
If you want the shallowest performance possible with your hull, you are looking at getting a cupped prop. A cupped prop, often with 4 blades, can be ran higher than a standard prop because it can work in aerated water. However, even cupped props still have to be far enough under the water surface to avoid blowing out. You'd have to talk to someone who knows props better than me to figure out the appropriate pitch to start with.
All that being said, I have a suspicion that your problem is that the 15 HP is too much motor to maximize shallow running in that hull. The faster you move, the bigger the hump behind the hull, so hypothetically you should be able to run shallower. However, as speed increases, that bigger hump gets further and further from the hull, so you need more and more setback take advantage of it. You can only increase setback to a certain extent on a 13' hull that is engineered for a 5 HP motor until you will damage the transom (longer lever arm, increased torque, etc, blah, blah, blah). That 15 HP probably makes that hull scoot and at WOT, your dinky little 4" of setback doesn't amount to nothing. The hump is probably 6-8" further back. At your slowest planing speed, you probably can set the plate 3-4 bolt holes higher and motor along pretty easily. Once you hammer it, your prop ventilates.
Nate