Welcome!
What a wonderful problem, I adore limes.
You can make a fermented lime pickle - I just googled a recipe, simply limes quartered, some juice and some Indian spices and leave in a jar in the sun for a couple of days. Put away in the pantry for a few weeks, then use with Indian foods.
You can squeeze all the juice and freeze the shells to use for marmalade. I'd make lime cordial if I were you.