I've been thinking about this problem for two days.
Alternator. Either it's not working or it's not wired correctly. If the alternator lead/wire is attached to the negative post of the battery - it will discharge the battery in a hurry. If the alternator is wired correctly, with the amp draw described, the ampmeter on the dash would be show maximum charge when the tractor is running. (Is the battery in backwards? Positive to starter, negative to ground)
Also, the amp load (battery discharge) described would almost certainly melt insulation on electrical wires. If the starter were bad,I don't believe it would sustain a 1600 amp hour load. 800 amp hour battey, 1/2 hour discharge, plus the alternator output = over 1600 amp hours. That type of sustained load would melt insulation and/or burn up the starter in a hurry.
There are two circuits involved in this problem. The starting circuit and the charging circuit, with the battery being common to both. Try this. Disconnect, unhook, the wire going from the alternator to the battery. With a freshly charged battery start and run the tractor. If the battery runs down in 1/2 hour the problem is in the starting circuit. If the tractor runs for an hour or two and will start again then the problem is in the charging circuit.