Jan, Concerning eddies (vortices), I think the fundamental aspect worth modeling is the behavior known as Tropical Instability Waves. These always form along the equator with a fixed wavelength of 1100 kilometers. That makes it a vortex train. This is at the top range of the mesoscale that you mention where horizontal dimensions generally range from around 5 kilometers to several hundred kilometers.
Regularity beats spontaneity when seeking an understanding. Mr. Drake should be looking at this if anything.
In the ENSO model, adding a TIW feature is a real parameterization with a wave number added to the mix which is 15 times the spatial resolution of the main ENSO dipole. As you say eddies can occur at a whole range of scales and any scaled standing wave that fits into the equatorial waveguide has a possibility to exist -- this is classical wave physics for cavity resonance from way back.