JKV, that sounds very odd.  Here in TP52-land (more carbon than a coal mine), we have mounted the Bullet below on the mast ring frame, and have the aerial tucked safely behind the mast instrument display bracket.  Works just fine huddled at the pushpit.  So I think adding extra APs won't fix the problem, and may actually make it worse by weakening the signal going to each AP.
I think Bullets like the shortest possible run of coax to the aerial, and I assume upstream of the Bullet is ethernet?
Have you tried a wirless strength monitor like NetSpot to see what's going on?  I use Splashtop rather than TeamViewer, no idea whether that would make a difference.

I am a novice at Exp but have some Unifi experience (not with the bullet, we use a ton of the classic Unifi APs). The bullet is extremely strong, and should have no trouble reaching anything on a boat. Its not strictly designed for access point use, its more like an AirMax infrastructure link between network parts. That said a lot of people use it.

If you have bad or intermittent signal, the forst thing I'd check is the antenna connection and the antenna itself (dont remove the antenna if its powered!). Check for clean connections and if possible test with another antenna (you need a simple one with N-type connectors).  90% of the time this is where a performance problem lies. The bullet wants its antenna directly on the casing, dont put any extra cables between. Also, check that the bullet and the antenna is not touching metal, as it can detune it. We use a lot of wireless antennas mounted on cars and boats etc, and we have 3d-printed a cradle that holds the antenna to the roof bars. If suspect this is the case just see if signal is vastly improved by moving it a feet away. Theoretically no metal should be within about 8-10" of the device. If all works, I'd expect a 600mW bullet to work within an 80 meter range over water.  

Thanks to everyone for their help. Problem was due to faulty antenna. Installed a new one and it works great.

-John