There is a principal mistake in your description, that linear filters are best for final critical listening.
Mixed and linear correction profile are not adequate for headphones. 90 % of the headphone’s effects are minimum phase effects and cannot be compensated by linear phase filters. The rest are mixed phase effects.
A headphone acts a single sound source and therefore has a minimum phase behavior. Only reflection effects occurring in the highs includes more sound sources and cannot be compensated by minimum filters. However, they also cannot be compensated be linear filters.
As a result, linear filters produce the worst phase response,
The available zero latency filter is the only minimum phase correction filter available, but unfortunately it is not as accurate as the linear phase filter.
I made intensive test with individually calibrated headphone over more than a year.
I got the best results with my one minimum phase filter derived from the sonar linear filter response outside sonaworks.
Second with the zero latency (minimum phase) filters inside sonarworks.
Whenever you enable linear filtering the sound stage gets more diffuse and the size of instruments tends to become bigger and less precise.
The tonal balance tends to get brighter.
Defining the needed amount of hall is much more difficult witth linear filtering than with minimum phase filtering.
Please make a minimum phase version derived from the linear filter available.
Please correct also your documentations concerning linear phase filters.