Workable Project Size

I'm also wondering what the content looks like.  The word 'banner' suggests large text with large areas of similar (same) colour.  There would be less advantage printing that sort of content with a dense DPI than compared to a busy photograph with fine detail.

You're going to need to print the banner, either as a single print or made from multiple tiles. The final file format used will dictate the pixel limit and file size limit.

"Close distance" is relative. Usually that means 1 meter or so for a large banner. So already you're down to a max useful resolution around 100 ppi. And "above lockers" indicates perhaps even farther away.

(Generally, the 300 number is widely misunderstood. It's not a magic number, even for book and magazine print. The origin of that number is purely technical: using a standard halftone screen of 150 lines per inch (lpi), it's the point where individual pixels can no longer be distinguished. It will be totally masked by the line screen. In other words, it's a theoretical upper limit, it's not a lower limit. And even so, it's a smoothness limit, it's not a sharpness limit. You can go below it without losing sharpness. In fact, the sharpness is determined by the 150 lpi screen.)

Generally 300ppi is only needed for prints viewed up close. I'd do some viewing tests with a small section, just print a sample and tape it up to see how it looks. You may be able to get away with 150 or less even at normal distances.