I've never been able to really resolve this issue satisfactorily, really. Perhaps additional hardening (steaming, aging, treatment with a chemical hardener) helps, perhaps it'll introduce new issues. For sure additional hardening will make washing more challenging with repercussions for the long-term stability of the print and highlight staining.
If I were to commit to this process (and I decided I didn't want to), I'd really just go the float method. It's how it was done industrially back in the day, it's how I see some of today's albumen printers work, so it's likely just the most fail safe approach.
You might give coating using cotton wool a try; it might allow for an even spread, some penetration of the sensitizer into the albumen layer without necessarily damaging the surface.
I personally found that thin layers of albumen are much easier to work with than heavier layers, but this thin albumen layers will only make a bit of an eggshell semi-gloss (which can be quite attractive), no really 'typical' albumen shiny gloss.