How can I play Pokemon USUM while living in the US on an European 3ds xl?

How can I play the upcoming pokemon games here in the US (I'm currently working here) using my european new 3ds xl. Buying a new 3ds xl is NOT an option.

Clearly I can't buy a physical copy of the game due to geo-blocking. Can I use the eShop on my Nintendo and buy the game there? Does anyone have any experience with this kind of situation?

Yes, you can.

I went to Japan and China last year with my (European) New 3DS XL and had absolutely no issues buying a couple of games on the eShop and playing them while overseas. You will, of course, need a credit card to do that; foreign eShop funds cards won't work at all.

Keep in mind that the 3DS eShop has a daily upper limit on how much you can buy (somewhere around €180-200), and your credit card most likely has a monthly limit.