... depends where you need to get to in Chelt.
The other way around for me, I used to live in The Reddings, and sometimes needed to get to somewhere in Gloucester. I think I generally used the B4063 through Churchdown, which as you say, is not a very good road, and past a Tewkesbury Borough sink estate, near RAF Insworth. Supposedly it was the estate that was as far away from Tewkesbury as you could get, and still be in the borough, so all the troublesome cases got dumped there. Prime Frod Escrot territory.
M5 btw fwiw.
Oh bugger, after living a good part of my life near the M5, when I moved to London I kept on referring to the M4 as the M5. Now I'm starting to do it the other away around.
A40 west of Gloucester is generally ok, but not pleasant in rush hour I would agree. Again there is no other good option by bike unless you want a massive detour via Highnam or somewhere.
I used to cycle along the A40/A48 towards the Forest, and as you say, it could be busy, but as long as you avoided rush hour it wasn't too bad, although I seem to recall a lot of the A48 had been "resurfaced" with that technique where they just chuck a load of gravel down onto something tacky, and rely on the cars to scrunch it into a vague representation of a good road. Horrible to cycle on for very long. This was almost 10 years ago, so they may have put down a decent surface by now.