Why not just boil the alcohol out of the other nonpolar solvent without basing it? You would precipitate the pseudo HCl out in the solvent, it can be filtered out of that solvent and dried, and if you still want to a/b it, you can do so without the alcohol being a problem.
You may also base an alcohol-pseudo-water solution, cover with solvent, and heat the whole thing up during the extraction to boil the alcohol off.
A little alcohol is not a a/b killer. The waterless a/b uses alcohol or acetone, depending on the pills involved. The alcohol is deliberately limited in the process to keep it from being much of a problem.
I have based alcohol/water/pseudo solutions before and extracted into xylene. I do this sometimes when I clean beakers I have used in the pseudo extraction/recrystallization process, and have a little of this and that in any beaker, without knowing how clean all of them may be. I will base this alcohol, add some water, stir well, and extract with xylene. I dry the xylene before gassing it, but I often get some unexpected chunks of pseudo by this process that might otherwise be lost.