Unable to export high resolution jpgs from LR

You cannot change the quality of an image file by changing the DPI (really it's PPI or pixels per inch). Regardless of what that setting is set to, the image will still have the same pixel dimensions, the same file size, the same image quality, no difference whatsoever. That setting will not change the picture content in any way. The only way you can have an image for large format prints is to have an image that has a lot more pixels.

Consider an image file that has 6000 x 4000 pixels. If you choose to print, for instance, an 8 x 10 or even a 16 x 20 print from such an image, it wouldn't matter whether the PPI was designated at 72 or 240 or 300 or 600. The image quality would remain precisely the same, and the print quality would remain the same as well. I've tried it with my own printer, and I've tried it by sending images to commercial printers. You cannot modify image quality by changing that PPI setting. The only way is to have more pixels.