I think you nailed it.
On a 440HO, (I've never had a BB):
If it was mine
I would put a 7-blade all-steel, hi-attack angle, fan on it, with a HD thermostatic clutch; PLUS a Hi-flow water pump and stat; and making sure the lower hose has an anti-collapse spring in it; and either swap the rad to anything that fits or move it forward.
In that way, when the engine is running, so is the stinking fan; and I never have to go thru life worrying about the stinking electrical system again. If it cools OK parked and at idle, forget the shroud. If it doesn't, then first I would look at the idle-timing and Transfer-Slot exposure, and if that is reasonably close, THEN go hunt up a shroud.
That is what I would do. ......
What you do is up to you......
If your engine is mechanically sound and your TC is not trashed, I can almost guarantee you that your cooling system problems are a thing of the past.
As to pulley sizes; While a agree with RatB, I feel that this is one of the last things to look at; but only because I have a 367HO with a manual trans,(no trans-cooler) and unlike an automatic, the revs are always up. Furthermore, I often shift mine at 7000 or more, and so, She does not need to be overdriven.
