I don't really understand the reason or rationale behind these questions, so here's some raw technical answers...
OctoWS2811 has a pinlist feature which lets you use any combination of pins on Teensy 4.1. Of course with the pre-made OctoWS2811 shield, you'd need wires to route the signals from other pins.
If you're willing to build some hardware rather than use the pre-made boards (part of the context I'm not understanding...), TriantaduoWS2811 is probably your best path to controlling a lot of LEDs using the fewest pins.
https://github.com/wramsdell/TriantaduoWS2811
On PSRAM, 2 chips is the limit, at least for their RAM to be used as ordinary memory. More can be connected by SPI, but you would need to write code to talk to them over SPI. There isn't any way to just declare variables or arrays with EXTMEM, as you can with the 2 locations on the bottom side of Teensy 4.1.
Usually EEPROM chips are I2C. Most of them have 3 pins to configure address, which limits you to 8 chips on each set of I2C pins. But they come in pretty large sizes. With SPI each chip needs a CS pin, and eventually with too many the SPI signals get enough load that you might need slower clock and/or buffer chips.
But again, not understanding your project, I can't imagine why you'd go to the trouble of so many EEPROM chips when you could connect 1 large SPI flash chip and use LittleFS.