External Memory Device for 8-Bit Computer?

I have found myself in possession of multiple (three) Z80 processors and a few sticks of RAM and ROM. I have built a working computer with said devices but I have an issue or two or three…hundred…okay, not that many. My issue is actually the (EEP)ROM, or the programming of, specifically. As usual with programming in general, I tend to need to store lots of raw data bytes into ROM but I don’t have a programmer. I can easily build one with Arduino (I’m in the process of writing the code) using two shift registers and just about every IO on the UNO but I ran out of breadboard space and cant find any of the other breadboards I own.

Anyway, I do have a programmer but I have to operate it using 16 switches (8 for data and 8 for lower addresses) and a push button and set/reset every bit by hand. What I’m looking for is a device that I can more easily store the program on and transfer it to the computer without needing to flash the ROM every single time, kinda like a CD/floppy drive, but as far as I am aware no such device exists except those. I would consider just placing a microcontroller on the board to handle device communication but I feel like that would be cheating lol; I want this computer to be completely self-sustained and I’m currently running it at a slow clock speed.

I might have an EPROM emulator in a box somewhere…

Alternately, you could write a serial bootloader and upload the program from a PC over the serial port. Have a Z80-CTC lying around?

I do not. I don’t recall ever hearing of one either. What is it, exactly?

It’s a 4-channel counter-timer chip; Zilog’s answer to the 8253

Sorry, mistyped. I meant Z80-SIO. Use serial comm to PC to upload your program.