PA-46 Pilot reported alternator problems and an off airport gear up landing.

Narrative

I fueled the airplane at approximately XA:00 pm CDT at ZZZ with ~85 gallons of fuel. After a run-up; Magneto check; and exercising the propeller. I checked all engine gauges and verified the annunciator panel was clear. Made the radio call to announce taking off on Runaway XX. I flew around the North side of the airspace at 3500 ft to towards landing to pick up instructor at ZZZ1 for some flight training. After getting about ¾ of the way there; the annunciator for the #1 alternator illuminated. I grabbed the POH to troubleshoot and recycled the Alternator with no help. I verified that I still had good bus voltage (which I did) and proceeded down to 2500 ft to get below class B airspace and provide a much more direct route to ZZZ2 and at this point; all was well with still just the #1 Alternator Annunciator light illuminated (still had good Bus voltage and no other indications noted on Annunciator panel). I continued toward ZZZ2; a short time later when I was well clear of ZZZ4 with all instruments and bus voltage still good. When I was past ZZZ5 and ZZZ6; the propeller surged significantly; and I then got the #2 Alternator Annunciator light and bus voltage started dropping significantly. I shed all unnecessary items; but then I was becoming difficult to maintain altitude and realized I wasn't going reach ZZZ2 or ZZZ7; so began looking for a suitable place to land; all while losing altitude and engine power. I noticed a large maize and set up for a landing. I landed without incident with the landing gear up. I had a smooth landing. I was obviously very shaken up and was shaking visibly.