I recommend you go to an hvac supply store in your area and inquire about a chemical to clean the hvac system and any surfaces you can get to. There are cleaning solutions for this very purpose and will also improve the overall system performance.
Here's one method using a commerically available cleaner made to sanitize your AC ducts system.
Clean Air Duct Treatment - How to chemically neutralize odors in your car - YouTube
There are other products available but this is how you would administer it. Probably find it at an autoparts store or auto dealership. Good luck
Most airborne problems like mold don't affect the stomach, or at least not rapidly. Kind of takes the flu, or something you ate.
Legionaaires disease does:
Legionnaires' disease: Symptoms - MayoClinic.com
How the infection spreads
Most people become infected when they inhale microscopic water droplets containing legionella bacteria. This might be the spray from a shower, faucet or whirlpool, or water dispersed through the ventilation system in a large building.
Cloged condenser drain.....
I had a case of giardia once that had those kind of symptoms. We had to wipe everything down with bleach. I'd make sure the steering wheel was cleaned well and wash you hands good before eating or drinking.
I would think you would see more lung problems if it were mold or bacteria in the venting system. CO is going to make you nauseated but you shouldn't see diarrhea primarily from it.
i see in the picture the exaust is exited next to the cab roof. my cab air intake for the ac unit is just under the drip line of the roof. it might be sucking in carbonmonoxide from the mufler. i bet the exaust you have was an extra option to have mounted that high. a lot of tractors muflers exit out the front so the exaust is lower than the cab air intake. so im guessing you might be suffering from exaust gasses you wont filter out carbon monoxide with stanard air filters.
G'day I would be inclined to think it is a bug in the a/c system you should have two filters just under the roof line and a recirc filter just behind the seat, I would go to an a/c repair place and they should have an off the shelf spray that you set off in the cab ( like a bug bomb ) whilst the a/c is in recirc and they are designed to kill bacteria and mould in the evap and ducting, After you have done this then replace all the filters, I don't think it would be the exhaust as this is the same type of setup that we use over here and have not heard of anyone complaining of your symptoms. Hope you get it sorted out it is too nice a machine to have sitting in the shed.