Which microcontroller to use to control Yamaha YM2612 arpeggiator?
YM2612

This chip was designed to be used as a peripheral to 8 bit CPUs running at a handful of MHz. When you look at the "datasheet" (just a pinout, really), you'll find that there are three groups of pins you have to care about:


D0 to D7
Control pins (CS, WR, RD, A0, A1)
IRQ


The data bus is bi-directional, the control pins are input-only, and the IRQ is output-only. It is obvious that this chip was originally designed to be mapped into the address range of an 8-bit CPU, but none of the devices you have on your list can do that (to my knowledge).

What you need

There are two features you want on your board that will make your life easier, and this rules out a few of them:


5&#8239;V I/O so you can hook the board up directly to the chip, without having to bother with level-conversion.
At least one complete 8 bit bi-directional  port so you can write values directly without having to split your data up and write it several times.
6 more pins for the control signals


This rules out the Raspberry Pi, the Arduino Nano, and some of the Teensy boards, and leaves the Arduino Uno, PIC, and some older Teensy.

I would consider these three more or less equivalently suited for your purpose. The latency problem you hinted is likely a newbie mistake, trying to use some software-delays in the Arduino. That just won't work for these things, you need a stable hardware timer to synchronize every write. You can do this with the integrated Arduino IDE.

Suggestion

Considering that you already have a PIC, and you seem to know how to program it in assembly (even if you're not yet comfortable doing so), I would suggest that this is your best option for a number of reasons:


Nothing is stopping you from programming most of it in C using MPLAB X, perhaps using a mix of assembly routines where you think it's required.
It has the requisite timers and interrupt mechanisms.
You already have one.
Depending on the PIC, you may be able to use its internal FOSC/4 clock output as your 8 MHz clock.