How to Quarter size Photoshop Files

A one-off pano like this is likely to be printed on a commercial inkjet, possibly as tiles (a large image COULD be printed on a web press or even with gravure, but that's extremely unlikely) and so it should be optimized for the printer/RIP combination that the service bureau is using. I would aim for 8pbc, 150ppi output and see if that works for them. This alone will cut way down on the file sizes and RIP time.

...which is already more than enough. 300 ppi is massive overkill for this.

It's one of the most persistent myths in all of digital imaging that everything for print has to be 300 ppi regardless of reproduction size. In reality, 300 ppi is a theoretical upper limit for book and magazine print to be seen from less than arm's length.

And it's not even an upper limit for sharpness, because that's determined by the halftone screen frequency (150 lines per inch in that case). 300 ppi is a limit for smoothness. It's the point where it's no longer possible to discern individual pixels in a 150 lpi screen, not even theoretically.

It can be eminently sharp at much lower ppi.

And then there's viewing distance:

This is often discussed on the forum, the fallacy of 300ppi being required for all print output.

There are technical and practical limitations. They don't need 16 bpc for output, so they would be reducing this to 8 bpc. They can't print from PSB and other file formats have pixel limits and or file size limits. They could arguably work with RGB which would also reduce file size.

For the output method and size, they know that 300ppi at 1:1 is too high for them to work with so 1:4 scale results in an effective resolution of 75ppi at 1:1 scale and produces "acceptable" quality output vs. the production constraints.

There are trade-offs to be made, one could argue that depending on image content and viewing distance/conditions that a higher number of pixels than 75ppi may deliver a better image, but this has to be balanced against production constraints (file format limitations, file handling, processing/print time).