[The Bard Rocks]

You are doing it right and are the rare one who actually knows what your range is. Either select your songs so they stay below that C or change the key until they do.

Most notation is written for the typical voice and that's not you. So in order to sing properly, you need to lower the key. It's necessary, but has disadvantages: if you are leading, everyone else with you must transpose to your key. But they can use a capo to adjust. You can't. It sometimes screws up the fingering as you have discovered. A potential solution to this for you is to use a baritone guitar as sort of a reverse capo which can enable you to retain the fingering you prefer and to make it singable.

Another potential solution is to search for songs that suit your voice well. That means many of the ones you like may have to be discarded, but it also means your singing can be much more effective if you make good choices. I have three friends who do this, and it limits their repertoire but, oh my, are they good at the ones they kept!

It's a "make lemonade when life deals you lemons" kind of thing.