SOLVED! After hunting through a ton of power banks on amazon I decided to try the one I have linked below and am very happy to report that it seems to work perfectly. When plugged in the projector acts just as if it were plugged into the wall.
NUCLEUS 26,800 mAh Power Bank, OTG Technologies, with 100 watt Power Delivery & Quick Charge 3.0 Technology. Power your Laptop, Mobile phone and MP3 player On The Go; Compatible with Nintendo Switch.
by Innov8 Communications Ltd