As an update, I found some helpful info on a few things I can look into doing:

http://www.phpbb.com/community/viewtopi ... #p12961708

Still not clear to me whether I can grant mods account approval privileges but I'll look a little more later.

Still haven't forgotten about this... the custom Q&A recommended is broken on this board, so I'll have to spend more time to figure out why or hopefully it's just fixed in a later version of phpBB, in which case I'll have to do an upgrade.

I also realized the current CAPTCHA image for registration is terrible, I can barely read the damn thing myself and it's not like it keeps out spammers 100%, so I switched it to a different one.

New experimental spambot countermeasures in place. One measure is that you have to answer a trivial question (related to the subject of this forum, naturally) that a bot or your average Russian spammer wouldn't be able to answer.

If this actually holds up and I get no spambot registrations in the next week or so, I may lift the approval requirement. So far so good but it's only been a day.