Don't know of any carrier that lets you choose either emergency row seats or bulkhead seats online.
Pedalbin you seem to answer your own question or is it just the way I read it?
Those seats/rows with bulkheads facing them and not adjacent to an emergency exit are normally 'blocked out' (unavailable online) as they are held for allocation to families 1st, generally (you were right to mention the bassinet). Emergency exit seats are never available online as the carrier or their representative (Ground Handling Company) have to view anyone who is allocated those seats in order to determine that they are fit and capable to occupy those seats and assist in the operation of the emergency exit if requested to do so by the crew, rule applies to all cabins First / Business / Steerage! Now if you're in First or Business then 'best seat' shouldn't be a huge issue really should it?
Emergency exits and bulkhead position vary tremendiously throughout the industry due to the particular layout chosen by the carrier. So the seats adjacent to the emergency exit on a BA B777 can/may be different to those on an Emirates B777.
If I travel down back in economy (has been known!) I always get to check-in early and specifically ask for my favourite emergency exit seat after determining what a/c type and config is operating the flight that day, if the check-in agent isn't happy to allocate I will ask nicely if I can approach the supervisor and work my charm best I can, never failed
