Yah, you've got two restrictions going on, the 5/8" connector and the 100' length. I think you're on the right track: 25' of 3/4" hose should see you quite a bit of improvement.
How much ya wanna spend? Here's a 25' one-inch hose. That should be able to wash your spa down the street!
Harbor freight has a 25' x 1" discharge hose, that rolls up flat for about 28 bucks. I wonder if that would work better than a 3/4" hose. It doesn't have to hold up like a hose, to stress and stain and UV. Just a few times a year, I presume, then stored away. There are even larger discharge hoses, like 1.5". I'm not sure that's the right tool for filling a spa, but they're cheap if you want to experiment. Discharge hoses
are made to move a lot of water.
Amazing deals on this 1In X 25Ft Pvc Discharge Hose at Harbor Freight. Quality tools & low prices.
www.harborfreight.com