Cat having trouble breathing

My 11 year old medium hair tabby cat is indoor only and he is a neutered male named Milo. About 4 months ago he got a blockage and spent 2 days at the emergency vet being unblocked. He has always been healthy so this was surprising and expensive. About 3 weeks ago he began to have breathing trouble. It started with him making this weird sounding noise everytime he inhaled. Took him to the vet and they examined and did x rays that showed heart and lungs were normal. He has a very slight murmur found 4 months ago. They suspected foreign body or nasopharyngeal polyps. Gave him an injected steroid that lasted about 8 hours and completely cleared up all symptoms but they returned the next morning. He was given prednisolone until a specialist could check for polyps or obstruction. The breathing issue continued on pred. Specialist found no obstruction or polyps but did find a small tear in tympanic membrane. He was sent home with a med for possible ear infection. He continued on the prednisolone taper but breathing has now gone from only having difficulty when purring or excited to ocurring whenever he is not lying still. Specialist raised prednisone back up to observe for 7 days. He has a clear nasal discharge and becomes unsteady when walking during a breathing episode. He is eating normally. Regular vet only said to put him to sleep unless i want to pay them a crazy amount for exploratory surgery. I am used to high maintenance pets as i have two bulldogs and just put another cat to sleep who suffered from IBD and hyperthyroidism his whole life. We still have milo and another cat who is showing no symptoms of any cold or respiratory issues. I have changed litter, am using hypoallergenic air filters, etc. Does anyone have any experience with anything similar. I hate to see him struggle to breathe as just three weeks ago he could run and play without issue. I am at a loss for how to help him. When he is sleeping his breathing is much smoother and he isnt trying to gulp air/swallow air or afraid to purr.

Poor Milo! I haven't had experience with nasopharyngeal polyps myself, but I looked them up:

https://www.acvs.org/small-animal/nasopharyngeal-polyps

Sounds like an operation is the best way to go. It's awful to picture a cat struggling to breathe like that.