...I've done tube upgrades on all of my tube microphones except my Mojave
MA200...that particular microphone shares a characteristic with your Groove Tubes GT66 (not having any "hands-on" experience with the GT66, but researching it's design online)...both mics utilize miniature pentode type tubes (soldered in place) rather than socket-mounted triode tubes used in many of the common tube microphones, which are much more easily swapped out...
...if your soldering skills are up to par, replacing the tube shouldn't be too dificult...the 6205 pentode tube
http://www.tubecollector.org/cv2432.htm
is not hard to find...reputable sellers like Brent Jessee
http://www.audiotubes.com/bjtubes.htm
offer a selection of vintage NOS tubes...and of course, Groove Tubes also offer replacement tubes...the downside is that "auditioning" tubes is virtually impossible due to the need to solder the tube in place (socket type tubes allow you to easily give various tubes a "test run" before chosing the flavor you like best)...therefore, purchasing a pentode tube from a reputable seller who thoroughly tests the tube before shipping, would be critical...
...a popular substitute for the 6205 is the EF734...vendors like Tubestore
http://www.thetubestore.com/noslist-0000-9999types-6000-9999types.html
and TubeDepot
http://tubedepot.com/tcp26.html
offer substitutes for the 6205...
...you're correct in assuming that rebiasing is not neccessary...so, put your electrical engineering skills to work (heat up that soldering gun) and start researching some of the NOS vintage tubes available...keep an eye out for "military spec" tubes, as these tend to provide the lowest microphonic characteristics...hope this info was useful...Good Luck!
PS...the upside is that these tubes are in very low demand (unlike the 9-pin triode tubes) so prices are bargain-basement level...under $10. for vintage military spec...