I only give 25mg of hydrox when needed. Maybe try only giving him that much?
As for the shots, your vet is not lying about them. I had the same discussion you had, almost exactly the same. We were traveling and seeing different vets (this was years ago for Sarah), and they would give her the steroid shot. Once I was somewhere long enough to get several, it was brought to my attention.
I told the vet that she is miserable without them, and that so what if she lived longer if she had a horrible itchy life!!! How was that an improvement?
The vet then discussed with me getting the allergy testing done, and from those tests they would create a serum to inject into her, over the course of a year. We also opted to have her nose wrinkle removed so her face could breathe. It was always wet and she rubbed it so much she was scabbed all over it ALL the time.
So maybe, just maybe, rethink this into a new thought, that potentially you could be heading down a new path to make things better for Vegas in the future. The steroid shots are masking the problem, maybe it's time to fix the source?
On the other hand, some bullies do not react well to the serums. It will be a slight gamble.
On that note, I would like to finish by telling you that when a bully has severe allergies their eyelids will likely roll due to swelling. So maybe Vegas has entropion only when he is under attack.
A final option is for you to come house hunting in Arizona :D. We have less allergens here!!! I need a bully neighbor who is as nuts as me!!