Yeah totally understand that reservation regarding getting it reviewed down the road. The fact that the reviewer doesn't understand this type of analysis however shouldn't really be a reason for not allowing it, if the code allows an analysis like this. Time to get a better reviewer at that point?! At least Mastan2 seems to tick all the boxes with respect to the 2nd order effects (initial imperfections, residual stresses, considering warping stiffness, etc) that need to be allowed for. This is of course provided you implement them in your model, which is another criticism of mastan2 that you start with none of the things you really need to correctly do the analysis being selected as defaults, another is printing anything from it is a chore.
I'd advocate you could simply keep these more detailed results to yourself (piece of mind for you as the designer) and present the simplification for review, and if its questioned present the more rigorous analysis (path of least resistance). This only works if both analyses show it works though, and you are often resorting to these more rigorous analyses because the simplified approach didn't quite work and there might be a significant benefit in consideration of the effect of the channel towards LTB.
I reckon if you knew the most critical member based on initial checks, that setting up the model and running it would take at most about 1-1.5 hours. I guess that needs to be held up against whether the result has some payback in terms of using less material/improved behaviour and can be tolerated with respect to the size of the project and the like. If this was a single isolated member, just ignore than channel and make it larger and move on, if it was used 100 times throughout a building I'd look at it in more detail.