The added bonus with bag balm is the menthol in it. I have read using peppermint oil too, maybe even on here, but that stuff stinks up a storm if you use enough to cover a birds combs and wattles.
Deep litter. Well as deep as I can go is 3" because I too have inward opening doors. I just watch the weather and clean when it gets warm enough. With wood floors covered by vinyl flooring, I can't dig down too hard or I rip the flooring, but it does allow for the frozen chunks to come up with a shovel and I break them up to haul out. I use shavings, not straw or hay which would be impossible to clean out until it thaws each year. I hate when they spilled their water or splash it out of the heated dog bowls and it soaks into the shavings, it just becomes a giant ice block of wood shavings.