Shouldn't cost you much more than 200 for labor and maybe 100-200 for materials. A "splice" is completely legal as long as it's a approved wiring method. What I would do is re-feed the tub from the disconnect. Simple and cleaner than adding a splice box or another disco.
Tell him 1500 and it's sold! But.. Here's the kicker. You will see a 40-50 a mos power increase and you have to run it in the winter. Can't just let it freeze up. If money is not a issue and you want a tub this is a good deal!
Sounds like you need to raise your sanitizer levels. High is good.. Why not drain and refill. Couldn't hurt. If using dichlor i'd do it every 2 mos or so myself.
The two hot colors don't matter as long as they are black, red or blue. Always use white for the neutral and green for the ground. Use stranded from the disconnect to the tub. Don't tape them together. 3/4" PVC is plenty large. If you go bigger you'll have to modify the knock out on the controller box in all likely hood.
If you're breaker isn't a GFI one I'd replace it first if you don't have a amp meter. Breaker = 10$. See if it fixes it. If not you have a tub problem.
I'd probaly just build my own supports. Some 4x4's or some 6x6's. Get a rotohammer and mount them in place with brackets. One under each corner of the tub bout a foot in would do it I would think. Structural engineer is the safe way.
If you paid someone to pore it get on the phone with them and tell the to fix it ASAP. I'd make them jack hammer out the pad and re-pour it. Concrete doesn't like to bond to other concrete.
Could you point me to some websites that discuss this? Personally, in the real electrical world, I've never seen nuisance GFCI tripping. Always there is a real problem. Whether it be a defective GFCI or a defective circuit or piece of equipment.