I am considering the idea of running a 540 rpm pto generator on the 1000 rpm shaft at 1134 engine rpm for extended periods of time. JD manual suggests minimum operating rpm as 1500. Does anyone have experience related to this? Perhaps those older engines don't lubricate properly at lower rpm? I'd love to hear of positive and negative experiences with similar setups.
Generally that is not recommended unless you are putting almost no load on the engine. Your engine is making little power at that low of an RPM. If it makes 65 PTO HP at 2075 engine RPM, it's making well under half of that at 1100 RPM as the engine is making much less torque at 1100 RPM than 2075 RPM. You would have to make the same torque at the lower RPM than the higher RPM in order to have the power decrease in a linear fashion as HP is the product of torque and RPM. If you overload the engine, particularly at a low RPM, it would be likely to overheat. Since it is a carbureted gas engine, it will probably also run rich as the carb is trying to dump a bunch of fuel into the engine due to it seeing little vacuum as it is under quite a bit of load, and you'll likely foul plugs and cause a lot of carbon buildup inside of the engine.
The other risk you run with running such a low RPM on your engine in driving a generator specifically is that generators are very picky about the speed they are driven at. Drive it too fast and you end up with too high of voltage and line frequency, and drive it too slow and you end up with the opposite. Both can ruin whatever you plug into the generator, although I suspect you are using universal motor saws, which really are only sensitive to the voltage changes and not the frequency changes. Running an engine so far out of its powerband makes it much more difficult for the carb to regulate the engine speed very well with changing loads than if you run it in the meat of the powerband where the engine can much more easily keep the engine RPM in a narrow range with changing loads.
A 2kW inverter would be a pretty big load and you would need to use this pretty sparingly. Drawing 1500 watts through the inverter will draw 125 amps from the battery, which is going to be well above what the alternator itself can supply. I looked in the manual for the 3020 for the alternator size and it wasn't listed, but it did list the battery as an 85 amp-hour unit. A new open station utility tractor of about the same power as the 3020, such as my 5075E, has a 70 amp alternator feeding an 85 Ah battery, so yours is probably a bit smaller.