Some questions regarding methods for solving pushdown automata problems
Your first solution is fine. I would not call this cramming into one state, it is kind of elegant to handle all this at the same place.
For your second problem, yes you can add 55 extra states. But also here you can use a single state instead, by coding that state into the topmost stack symbol. Simply have many stack symbols $A_0$, $A_1$ to $A_{55}$ (or so) and replace $A_i$ by $A_{i+1}$ until 56 is reached.
In general every pushdown automaton can be replaced by one having at most two states.