Just my opinion, so take it for exactly what you get from it.

I would be inclined to strip it off and start again. When I am
finishing, I have had all manner of results with BLO as a finish. Now
if you put a couple of coats on the paint and left it, you would
probably be fine with a simple prime and recolor.

But the BLO is a different part of the equation. While it may be dry
to the touch, it may take a few weeks (as in 4 - 6) to cure out. You
say you put on a couple of coats - two heavy ones? Two light ones?

With humidity, temps, brand of BLO etc., being factors, the longer you
wait to recoat the better. I have put primer/sealer over BLO in an
effort to stabilize it, and failed miserably, both times. It simply
leached slowly through my primer.

I also see that on your second attempt, you will be putting wax on the
finish. (Wax on painted furniture?) Anyway, if you waxed the first
attempt as well, it isn't only silicones that you will contend with to
get your finish right.

You will also have to contend (depending on the quality of the wax)
with just how much waxy resin is left behind when you buff off. Paint/
primer doesn't stick to wax well, no matter how you try to sand it
off.

Stripping is the only way to make sure you do it one more time. If
you are like me, I would be undone if the finish didn't look right or
the pigments/BLO leached through my finish. I would then have to
start from square one and do it all over again anyway.

Robert