Slow taper to avoid insomnia?

I have been about a 5 cups of coffee a day drinker for quite a while, and recently did a quick taper down to zero caffeine without too much issue initially. Had the usual headache and lathargy but this passed after a few days. My sleep was initially better but after about a week of being caffeine free I got insomnia which I understand is common when going decaf and can last months.

I've experimented with introducing a small amount of caffeine back to try and deal with the insomnia, I'm talking one cup of black tea a day, and it seems to help with the insomnia some what. I'm considering sticking to a single cup of black tea a day for something like 2 months to really get my body used to quite low caffeine before finally going zero caffeine at which point hopefully the insomnia will not be considerable given my daily caffeine dose was so low.

Does anyone have experience with this method?