I know bugger all about doing this with hop flowers, but that actually makes sense to distill them as if you were making perfume or essenses from herbs etc.I think a better way to combat the bitterness is to use a commercial steam distilled essence. No bitterness in those AFAIK.
Distilling essential oils as you would be with a hop flower is perfectly legal, them other things you can do with a still, well im not sure.If the legal distillation of essences is an acceptable topic here and not breaking any rules i can say i have a legal 1 litre glass still for doing essences, but no knowledge on how to extract the oils using it.
It's powered by an open flame though and i don't think i have enough parts to convert it to steam power without getting it out and having a look at where i could put some hop material after the boiler. Maybe i could make a small stash in the column section with some muslin.
If given some advice i could certainly give it a go and report back.
If it's against the rules then i don't have such equipment at all and am only talking in theory, in fact i didn't even type any of this.