Hello,
I think moving him up to the 55 would be good, and you could attempt to add some more cichlids with him (although he is one of the more aggressive species and is a big guy- might be violence from him)
A few things stand out to me when reading your post
1- Should be doing much more than 5% water change bi-week. More like 50% per week for a fish this size in a 20 gallon. I would bet that your nitrates are very high, which probably caused the bloat. I'd start doing the 50% weekly right away.
2- I would not put a "pH balancer" in the tank, sounds like snake oil to me. If your water is hard because of the limestone, pH is probably high, and that is perfect for African cichlids like this one
3- I would recommend buying some seachem prime or other dechlorinator, yes chlorine will gas off in 24 hours but chloramine is commonly used nowadays and will not gas off as quickly, stays in water. Better to use a chemical to neutralize the disinfectants in water.
4- You say you want to transfer his old water to the new tank- this is not helpful, no beneficial bacteria lives in the water itself, it lives in the filter and on surfaces in the tank. Bringing his old water would be less beneficial than using new water, since the old water will have nitrates built up in it. The thing to do, is set the new tank up with 100% clean water. Then move the fish and the filter over at the same time, without cleaning the filter. the bacteria will continue to live in the filter. Just make sure the new water is about the same temp, and is dechlorinated.
5- Not sure how you are cleaning your filter, but you don't want to be replacing 100% of the media ever. When you do your water changes, keep a bucket of the used water after you take it out of your tank. Then just take everything out of the filter, and swish it around in the bucket with your hand. Rinse it in the old water- if you use tapwater, it will kill the cycle bacteria. If you completely change the media, there will be no bacteria on it and water will turn toxic because nothing to turn ammonia to nitrate.
I would have a read of this, it is bread and butter of keeping fish, something everyone needs to know
https://www.fishlore.com/NitrogenCycle.htm
Sounds like you care about the fish quite a bit. Awesome! Get his tank clean and get him upgraded, will be much better for him.