I ve never had the issue with all chain ride and no swivel. And I anchor a lot, year round, well over 100 times a year
If you think about it, a swivel does nothing to prevent the chain from twisting, all it does is keep the anchor in the right position to get on the roller. The only way the chain can twist is if it was all dumped in locker instead of being fed in
Are you sure it s the twisting which is preventing the chain from coming out? Sometimes if a pile of chain falls over, it can get tangled up, although very rare
You can't do much in the locker and digging the end from under the pile is not easy. Best solution is to drop the hook in your slip and help the chain out Once the anchor is on bottom and the chain is slack, pull it off the gypsy and pay it out manually thru the hawse pipe. You may need to pull the cover off depending on the windlass. once it s all out and you use the windlass to bring it back in, it will naturally untwist. Remember the gypsy will force it thru evenly, and the 15 or 20' you have out is enough distance to untwist it
Pulling the gypsy isn't necessary to get the chain out, if the windlass is install correctly all you have to do is pull the chain off the gypsy