After examining all the photos again, I must have missed the one earlier on the hooks on the bucket. Good job of getting them around the bale. LOTs of work but effective and by having the bucket tilted up, you stay fairly close to the tractor. I dont think those loose wrapped bales will weigh more than 800 pounds when green (freshly baled) and certainly not 1000 pounds when dried out for a few month. A 5x5 bale has to be tightly baled to weigh 1000 pounds.
A bush hog is likely the best at using its weight effectively to counteract FEL forces. It gives you plenty of counter weight for task with the FEL but it does make the tractor train fairly long so it isnt very maneuverable in tight spots. Even a light weight 6 foot bush hog is going to weigh about 800 and being hung far back from the tractor gives you much more counterbalance than the same 800# on the lift arms between the pins like a ballast box is. I dont think you can beat a back hoe for counterweight, but at $7K purchase price or more, it is expensive counter weight.
Regarding 3 PH bale spears, they can be found really cheap (around $100) on Craigslist but the real drawback to them is not only can you not stack with them, but you cant unload a trailer with them either. They are only good for moving them around from ground level. So until you can get enough saved to put on a QA attachment on your tractor so you can swap attachments and purchase some hay spears or pallet forks, I think you have the best idea already for moving them. Now if you could just get those straps under each bale when they are being loaded on your trailer, then you would be good to go when you got home to unload. You wouldnt necessarily need but one of those straps in the center if is was cinched down tight as those straps look like the 10,000 pound rating ones that I have, way overkill for a <1000 lift. A 2500# rating would be more than enough. It might swing around a bit though with only one strap which could be trouble , but you could add a tag line (rope on one or both ends that is tied off to the FEL) to keep it from swinging.