I play a lot of Irish and Welsh music. Quite often, these pieces are in G major (one sharp) or D major (two sharps). I still tune my harp to E flat major.
Than I am ready for all the sharps I really use, and can still play in the first three flat keys.
This could help. Your harp has already adjusted to being in tune in E flat. You can always stay in the key of C, but it will take time for your harp to get there.
Good luck! Holly