First,
Lots of good ideas, and intentions too, but a hot start issue should be fairly straight forward to figure out. I can feel your pain on trust with dealers - I am a inter-provincially licensed auto mechanic myself, and know WAYYY too many shops that will steal your blood if they could get away with it.
When hot starting, your bike turns over very slowly instead of normally? Perhaps even coming to a "lock" and not turning over at all? But when cold it turns over and starts normally? If so, your engine is building higher compression once warm. As the pistons heat, they'll naturally expand. This allows less clearance between them and the cylinder walls. This also adds friction. Fortunately, this means your engine was built pretty tight. I can't put a warranty on anything I've never seen, but I expect you'll get many more miles out of that one vs. a "loose" engine.
The "fix" is a little more complex. Possibility #1 is that the battery is actually weak, and not supplying enough current to turn the engine with the extra resistance of a hot motor. This can be verified by using booster cables to your car battery
with the car engine not running. Doing this will supply extra current but no extra voltage. If this solves the problem, look at replacing the battery with (hopefully) a better one.
Possibility #2 is there's resistance in the heavy cable between your battery POS terminal to the starter solenoid, or from the solenoid to the starter motor. You can test this with a voltage drop test, or simply have better cables made at your local performance car-stereo shop. Expect to pay between $25 & $40 for these cables, more if you have the shop install them for you.
The 3rd possibility is that the starter itself simply is not strong enough to turn over the high-compression motor when it's hot. This is a common problem on hand-built, muscle car motors. I do not believe a high-torque starter motor is available for the Busa, but you could purchase a stock unit and have an Alternator & Starter repair shop rebuild it for you for more torque. This would involve dismantling the starter and rewinding the armature - not to be done at home. I recommend getting a replacement stock unit for the donor, because rebuilds like this often take more than a week. The last alternator I had rebuilt to put out more power (again, a car stereo) cost me $120, plus the donor alternator.