(In reply to solution to part 1; thoughts on part 2
Part 1 is easy.
Part 2 is a D4 question, to which I do not have an "official solution". Since you show a procedure leading to a final answer and it is limited only by size I suggest that you provide 2 "modified" answers:
1. Part 2 - an exact answer , applied to Hawaian alphabet.
2. Part 2 - an answer re English ABC, providing intelligent apprroximation (like log a(26).
IMHO - the result of part 2 qualifies to give you credit in OEIS, - the table does not need to reach big-big numbers.