So far I have just added Emitter degeneration resistors
Oh, well it's not an OTA anymore...
You get OTA functionality from the nonlinear r_e. When R_E is fixed by swamping with an external resistor, gain saturates and output is no longer proportional to the control current.
(If you meant for the mirrors, not diff, that's fine!)
Distortion can be reduced arbitrarily by reducing the input signal level, but eventually noise will dominate. OTAs are not renowned for SFDNR. You may be better off with an MDAC architecture or something like that. (If you don't want steps, the steps can be interpolated with an OTA or JFET; distortion of the active device is reduced by way of its being a smaller part of the final signal.)
Nexperia do some reasonably priced matched transistors, some of which come connected up as a current mirror already in the package.
Note they are separate die parts, and the datasheet specifies typical mismatch under load conditions.
This can be alleviated (by about a factor of hFE) with a cascode structure, e.g. Wilson current mirror.
You have one advantage over the classics (e.g., LM13700), good PNPs. Otherwise, the matching and temp tracking is pants.
I was going to simulate the circuit and vary some of the matching ratios between some of the transistors, to see how matched the transistors need to be and how this affects the performance of the circuit.
Don't forget to adjust TEMP as well as W. (Ideally TEMP would be a function of device power and thermal time constants, but that's nontrivial to do.)
What I am struggling with is choosing particular transistors to use in the simulation, obviously the end design is limited by the matched pairs that are actually available, so that is a good starting point. After that, the main variation between devices is just the typical Beta or hFE range, how should I select transistors based on Beta aka hFE?
It really doesn't matter. You're after the basic (Ebers-Moll or Gummel-Poon model) behavior. You can use the default SPICE model if you like. Any general purpose transistor, near what you're going to use, will do. Power transistors will have too much capacitance, and may have too little hFE at low currents (if recombination is even modeled). Other than that, you have a good 6-ish
orders of magnitude to work within.
Tim