If he is fit enough for it, you could consider surgery. It's a quick and permanent fix. If not, then I'd say you're already doing all that you can. Swab to make sure you're treating with the correct antibiotics is always recommended, sooner rather than later, so good that it is getting done!
Little things in day to day life is just using food and water bowls that kan be cleaned effectively every day. No plastic bowls as they kan have scratches that harbor bacteria. Wiping away food or pus of anything that collects in the lip folds. If he has any toys that he likes chewing or carrying then probably keep them as clean as possible too. Probably things you already know, but it's the only things I can think of.
Hope the results of the swab and culture gives you a more successful treatment! My girl was much younger when she had this, but after months of trying "everything", I finally decided to do the surgery. It's not particularly invasive as it is just removing the affected skin and closing with a few stitches. So really it comes down to the risk of anaesthesia. Recovery was nothing compared to the infection.
There are gels that contain clorhexidine too, they are sometimes more effective than hibiscrub because they're left on the skin longer. You could ask your vet about that. I have no idea if they are safe to use near the mouth. But things like clorexyderm spot gel (dr.baddaky)could help if it is safe to use on the mouth. If not, then stomodine is used in the mouth so definitely safe, not sure if it's strong enough though. Ask your vet about it, they probably know or can ask the manufacturers if they don't know.