I think I would build and install perl separately on each of the 10 servers (using same configure specs), then write a script that installs all required modules, and then run that script on each of the 10 servers.

That should avoid the type of problem you're experiencing with DBD::Pg. If you really want to just build once and then distribute, the only solutions to your DBD::Pg problem I can think of are:
1) Build DBD::Pg (and the others) against static libs;
2) Place a copy of libpq.so.4 (and the other shared libs) in the same directory as the perl executable.

Not sure that either of those two last options will scale terribly well. The second solution also assumes that the perl executable will be in the path on all machines.

Cheers,
Rob