The governor has nothing to do w/ timing. But I'm sure the cleaning was helpful.
" it tends to bounce +- 2 deg and never maintains a specific degree setting. "
At what RPM?
There are three settings.
At idle, the light should flash & the marker should line up exactly at 4* if you did the static timing correctly.
If not, loosen the distributor & turn it until the marks line up. It should take very little adjustment.
Once you've got that done, increase the engine speed to 1200 rpms. The light should flash & the marker should line up w/ the 10* mark. Then, increase the rpms to 2000 & look for the marker to align w/ the 17* mark.
Close counts on the advanced timing. A degree or 2 either way is ok. But, no movement or 5* or more off means you have an advance weight problem. You don't adjust the distributor to fix that.