Would it not have been more efficient to beam directly and simultaneously aboard the BOP as the Klingon party beamed to the Enterprise? Both ships' shields were down, I mean even if the BOP still had working shields it needed to take them down to beam it's boarding party over. This would have left Kruge and Maltz as the sole occupants of the BOP against Kirk, McCoy, Scotty, Chekov and Sulu and from what we've seen, Kirk could possibly have handled both Kruge and Maltz alone.
In fact, why did Scotty not just lock onto the entire BOP crew and beam them into the middle of a volcanic eruption on Genesis or easier - space? Problem solved, they could then beam over to the BOP and use it's sensors which were already locked onto the surface, beamed up Spock, Saavik and David (his body, but maybe he would have survived had Kirk not wasted time talking smack with Kruge instead of pulling the old prefix gambit) by isolating anything without Klingon blood (sure, they might have picked up a few evolved microbes, but that would surely make for a delicacy right? Bonus!), scavenged the BOP for spare parts and repaired the Enterprise and then warped to Vulcan as they all had a good old laugh about how easy it was to steal a Federation starship, make it to a locked down sector of space and then defeat an entire Klingon crew with a malfunctioning ship!
Seriously, why not?
In fact, why did Scotty not just lock onto the entire BOP crew and beam them into the middle of a volcanic eruption on Genesis or easier - space? Problem solved, they could then beam over to the BOP and use it's sensors which were already locked onto the surface, beamed up Spock, Saavik and David (his body, but maybe he would have survived had Kirk not wasted time talking smack with Kruge instead of pulling the old prefix gambit) by isolating anything without Klingon blood (sure, they might have picked up a few evolved microbes, but that would surely make for a delicacy right? Bonus!), scavenged the BOP for spare parts and repaired the Enterprise and then warped to Vulcan as they all had a good old laugh about how easy it was to steal a Federation starship, make it to a locked down sector of space and then defeat an entire Klingon crew with a malfunctioning ship!
Seriously, why not?