IMHO, going up in size in an attempt to address a depth issue is not a good idea. It's trading one issue for possibly another issue that's an even worse issue to deal with, skates that are too big for you. Often, skates that are too big will cause the wearer to crank down on the laces in an attempt to stabilize the foot in the boot, which will cause similar issues (lace bite) as one could get from skates without enough depth.
From my experience, here's something to consider. I have extremely small feet for my size. 5'5 adult with size 4.5 skates. No retail skate on the market has the right depth for me. For me, the best thing other than customs was to get the skate that had the right dimensions for everything else except depth, and then figure out what to do about the depth. And over the years, I figured out how to prevent lace bite for myself. First up is I use Option B skate straps/eyelet extenders. This adds depth to the skate and distributes the presser more evenly across the foot. Second, I learned to skate with loose/looser laces. The latter, for me personally, is the universal solution that will carry across all skates I buy from now on. Also, it has had the added benefit of making me a better skater overall. It just took a little time, a little patience, and a little work.
Don't know if this is the right thing for you, but it's just something to consider.