Nice!
The original steppers (28BYJ48) have centre tapped coils, so are rather simpler to drive than the NEMA17 four wire ones.
You can get unipolar (six wire) in NEMA17 sizes, which reduce the complexity a bit, but the motors require current limiting regardless of drive type - either a ballast resistor to limit the maximum current (which uses a lot of power and dissipates a lot of heat), or current control at the driver. Making drivers will be relatively expensive either way.
I think your best option is to use four wire motors and mass produced modules to drive each motor; A4988 based ones are available for less than $1 each in tens.
eg.
Smarter Shopping, Better Living! Aliexpress.com
Those should be the same pinout as these, which have rather more details in the listing:
A4988 Stepper Motor Driver Carrier breakout board for Allegro’s A4988 bipolar stepper motor driver. Adjustable current limit, 5 microstep resolutions
As with the first diagram on that page, everything can be fixed wiring for each motor and power, with the modules just needing two unique logic signals each for step and direction (and the logic ground connection).
That means you could control four motors from a normal logic-level eight bit shift register such as a 74HC595, and chain as many of those as you want to control multiple sets of motors on one SPI output from an MCU.
With SPI running at eg. 10MBit, the update time would be only just over 3uS for 32 bits, four cascaded registers controlling 16 motors total..
You would need two updates for each step stage, one to set the step bits high and another to set them low; still under 10uS.
In each sequence, only set the step bits for the motors that have to move at that instant.
The whole thing could easily run at 1000 updates per second with plenty of time between output sequences to do the pattern move speed calculations as to which motors require a move and when.
For an MCU, I'd suggest an ARM based arduino compatible board such as an M0. Using SPI as the main outputs, you don't need many I/O pins.
eg. These are cheap, program with the Arduino IDE once you add the seeed library files, have SPI that can run at 12Mbit I believe, with 256K Flash and 32K RAM:
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Getting Started with Seeed Studio XIAO SAMD21
Or with WiFi included:
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Wio Lite W600 is a cost-effective Arduino compatible board with the W600 WiFi module. The Wio Lite W600 features Atmel® | SMART™ SAM D21 ARM Cortex-M0+ based microcontroller and the W600 WiFi core is a 2.4GHz WiFi module features ARM Cortex-M3. Since the Wio Lite W600 uses SAM D21(the same chip...