The A3 is hard to get and pretty rare. I would not bob it, but would have rebuilt and bobbed an A2. However, your truck and $$ to spend. Keep the pics coming, make it special, really special, if you do bob it, so it is not just another bobbed deuce, considering it is the A3. For an doing that with A3, it ought to be done so it's something that makes CXT owners cry.
About the a/c, the cab has a lot of air leaks and heat soak, even after you seal it up. I don't know the LA climate but if it were for me in TX, I'd put a 30,000-36,000 BTU unit on board, driven by the engine. Or a modified 2-ton window unit in the bed driven by an aux diesel genset. I see you want to use the 300A alternator, well OK, but that means that you will need to run the engine to make electricity, then convert the electricity, then run an a/c, which is basically a motor turning a compressor.. Lots of places to lose power/efficiency. Also the starting surge on a respectable a/c can be quite a lot.
The next thing is that an inverter, unless it is a sinewave inverter, makes a waveform that motors do not like, and you may have further inefficiencies or motor heating issues (I2R and reactive losses) with the compressor and fan motors unless you can clean up that modified square wave a lot.
If you mount a window type unit, be aware that the constant vibration from driving can cause the copper refrigerant lines to vibrate and crack or wear hols in them if against something. Also, the blower motor for the condenser and evaporator - -its mounts are likely rubber and may sage or move enough as the truck moves and bounces, to make the blower wheel or fan baldes hit the volute and that makes a bad noise as well as can knock the fan/blower wheel out of true causing shaft vibration hastening the eventual doom of the a/c unit. Those problems are exacerbated in the larger units>1 ton. I had these things happen and the solution was to rigidly bolt everything in place and wrap all lines in armorflex and fasten them in place.
OK, well keep the pics coming.