cal55,
The HEI would not require any bypass circuit, so that theory is out. Because of the close proximity of the header pipe to the starter, starting problems are fairly common on these engines. If the starter is worn out, or marginal at all, excess heat will sometimes make a hot restart tough.
If you wired your meter to the START terminal, it would go dead when the key sprung back to RUN wouldn't it. Turning the key to OFF should kill any power to the HEI...that's how the engine is shut down. If there is any path through the voltmeter that allows power to the RUN terminal of the keyswitch, the ignition would still be powered even though the key was switched to OFF.
I'm not sure how you wired your meter, but it might be something to check. Keep us posted.
Stuart