Don't waste your time on check-in jobs. You will have zero contact with crews and learn very little of any use or relevance. Similarly with baggage handling.
As Silverknapper says, cabin crew work is unlikely for a short period as the airlines put in a significant investment in your training, and they won't waste it if they can get somebody else who wants it for the longer term. However, I would gladly swap my roster for an EZY CC roster.
Dispatch is your best bet, although be aware that the money is rotten and you will be expected to work shifts over a 24 hour period, so there is limited flexibility for other activities. Loads of contact with crews, and they tend to take an interest in you and your career progress if they like you on a personal level. Just try not to upset too many of them as this really is a very small industry and you will earn a bad rep very quickly. Enjoyable way to waste time and won't count against you at interview. I have numerous friends in FO positions who started out in dispatch thanks to the job market post 911.
I can't speak for other stations, but it is nonsense to suggest that you cannot go straight into dispatch with zero experience. That is exactly how it works at NCL. Almost none of the dispatch team in the office came to the job with any prior experience on the ramp. Always vacancies up for grabs. PM me if you want some contact details or to know what you will be letting yourself in for. Your aviation ambitions won't count against you either - there have already been 4 CPL holders through the office in the last 12 months alone.
Also at NCL, there are no operations departments as the airlines use the ground handlers for all services, so the only non-crew airline jobs available are in customer services type roles and again, you will have virtually no contact with crews or any involvement with the operation airside.