I am postulating a full-height quarter-wave 40M vertical that is
switchable (relays halfway up?) to a 20M vertical dipole.

Seeing as how my two favorite bands are 40M and 20M, seems to make
sense to me, but googling to see if anyone else has done this sort of
thing in the past doesn't give me a lot of hits. Is this workable? I
am not yet ready to go (budgetwise or real-estate-wise) to a real 20M
beam and I'd like to increase my oomph for DXing on 40M (right now I
have a wire dipole in the trees and am having a blast).

Looks to me I could build an extremely lightweight small 5M high tower
with a 5M metal mast on top. (I know, real conductor diameter will
mess those numbers up a little bit). And a relay between the mast and
the tower would either put them in series for feed as a quarter-wave
40M vertical, or separate the two and let me feed halfway up as a 20M
vertical dipole.

How would the ground radials used on 40M potentially mess up the use
as a 20M vertical dipole?

One idea for a lightweight 40M full-height tower/mast vertical with
insulated-from-ground mounting is shown at http://svc.cc/antena.html

Tim N3QE