The end portal is hardcoded, that's because it's a parallax effect... (it changes based on time and the moves in relation to the player as if it is "bigger on the inside"). This is all done internally (not with model files even for just using a 'generated texture')... So there is no real way to setup calling that specific effect.
The closest you can really get is /setblock ~ ~ ~ minecraft:end_gateway and that is more like a pre-rendered form of the end portal parallax with only a small portion visible (rotating with your view) rendering where the block normally would. The end gateway doesn't have a model file either...
In the future this may be possible using shaders. It seems shaders are a little more powerful than they were, as they now can target mobs (hint: the spectral arrow is done using a shader, but shaders could not previously modify the unseen like mobs behind walls), but I'm not aware of specific hookups for things like blocks/particles where it would be useful.... and I don't think shaders can yet be stacked (because the 'super secret settings' button was removed... possibly because they would break/be broken by spectral arrows). If it is possible in the future, the end portal will likely be ported over to a shader.
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"I'm an outsider by choice, but not truly.
It’s the unpleasantness of the system that keeps me out.
I’d rather be in, in a good system. That’s where my discontent comes from:
being forced to choose to stay outside.
My advice: Just keep movin’ straight ahead.
Every now and then you find yourself in a different place."