Many thanks for the quick reply, Martin.

Will the following work if I want a provably correct result
(when mylimit is a proven upper bound on the size of G)?

H:=ShallowCopy(G);
StabChain(H,rec(random:=800; # or whatever
                limit:=mylimit);
if Size(H) = mylimit then
    G := H;
else
    StabChain(G);
fi;

Does StabChain ever change an existing component of the group record;
that is, should I make a Copy instead of a ShallowCopy in the first
line?

Regards, Leonard.