I am quickly running out of space on the SD card I have installed in my Switch. I was wondering if there is a way to maximize my internal storage situation.

Currently I have no games installed to the internal storage, only screenshots, video captures, etc. I have a 128gb card in my Switch, and since everything installs to the SD card by default if you have one installed, all the space on the Switch itself goes to waste. Last week, I installed Doom. It takes up over 20gb of disk space. If I were to delete the game, remove my SD card, then go to the eshop and reinstall the game, presumably it would then install to the Switch's internal storage, right?

yes, it would. I have to believe that you can decide each time where to install a game, but I haven't tried it