Looking only at the vacuum specific impulse of plain hydrogen-oxygen
rockets, is it possible to advance their specific impulse to 500, or
even 520?

For example, I recall Mr. Spencer recently mentioning that an ideal
oxidizer:fuel ratio for hydrogen & oxygen was 4:1, but 6:1 was used
because of tankage mass penalties. Would a 4:1 ratio provide an
increase in specific impulse? If so, approximately how much?

The highest Isp I could find was 480 sec for the Advanced Expander
Cycle engine, a testbed; I recall some sort of development effort in
the 80's that was talking 490 sec and was having problems with the
turbopumps having to spin very, very fast to generate enough power
and pressure.

snip

The highest chemical engine Isp I've seen is about 520-530... it was done
using a three-propellant engine (of which one propellant was fluorine).
Now, there are many problems inherent in using fluorine... extreme toxicity
and reactivity the chief ones (fuel that wants to eat up the tank it's in
isn't all that great). In short, a nice experiment, but impractical.

I did see a proposal at the JPC last summer for a TSTO using such an
engine... combined, though, the 2 stages used 6 different propellants (not
counting on-orbit RCS/OMS fuel). Not good from an operability standpoint,
and still the fluorine problems (which he claimed to have solved).