Would putting it on a drive work or does the different focal lengths need different settings
Yes .... an ordinary scope star tracking drive should enable you to get exposures plenty long enough. There is a small complication due to the moon not moving at the same speed as the stars (because of its orbital motion - and the rate isn't constant) but you for a maximum permissible exposure you can change the 500 in the formula to 5000 (at least) if tracking at sidereal rate i.e. 10 secs at 400mm will not be a problem.
Some scope mounts enable you to set a "lunar" rate; though (as the orbit isn't circular) the actual rate required is slightly variable, this should enable you to take very long exposures of the moon without trailing. Possibly useful during lunar eclipses (but there aren't any for a while!)