Will this generator run a 13500 btu ac

[videoarizona]

The watchdog, like many instruments like it, can't react fast enough to give you the true AC startup spike current. Your startup current spike is going to be anywhere from 30-40amps depending upon age of AC unit, etc..
I love my Watchdog, but only rely on it to keep me safe.

My Victron DC shunt does show the spike currents on the battery. Does so on a graph. A good AC shunt should do the same if you are interested.

Otherwise, good info to see. My current draw in similar situations is close to yours.

[extrachrispy]

Steady state, my Coleman Mach A/C pulls about 1800W when the compressor and fan are both on (as seen on my own Power Watchdog). The startup wattage will be close to double that, unless you install a soft start (I have not yet done this).

Your generator is going to be marginal. It might work, but it might well also go into overload shutdown--it definitely will when the A/C starts (without a soft start).