If you are cutting a total of 12 acres and not doing it every two weeks, then I think the rotary cutter is your best choice. Finish mowers do not handle tall/tough weeds well and you will have a much slower speed making the job take much longer. The wear and tear on your mower would be higher and you'd spend a lot of time doing blade sharpening and maintenance. A rotary cutter/shredder seems the obvious choice for this job.
You can get some impressive results with a rotary cutter if you keep the blades sharp. Actually, you will probably find your blades only have to be sharpened once per season if you only cut grass and weeds with no rocks or other hard objects. Rotary cutter blades are very thick and tough compared to mower blades.
I think the advice of running your cutter at 1000 rpm is rubbish. I'm not sure what the person meant, but a cutter is designed to run at your tractor's 540 rpm setting. If you run at a higher rpm, you'll surely damage the cutter and be causing a very dangerous situation. I don't even know if your tractor's engine could run at a high enough rpm to produce 1000 rpm at the PTO, probably not. You either misunderstood the person's statement or that person is very, very misinformed.
A mower has much smaller blades and runs at a higher rpm. The average push mower for yardwork runs at the engine rpm of around 3000 to 3600. The blades have fins that cause a suction on the lawn and the sharp blades cut the grass smooth. I'm not sure what a tractor type finish mower's rpm is, but I'm sure it is very fast (probably around 2000 rpm) and the blade design is similar to the push lawnmower or a riding lawnmower's deck with multiple blades. The idea is to cut the grass into tiny pieces and deposit it back on the lawn as mulch. It just does not have the brute force that a rotary cutter does.
I think you'll be happy with a rotary cutter. If you maintain it well and keep the blades sharp, you'll be able to keep those 12 acres looking very nice. they won't look like the fairway of a golf course, but they will look like the short rough, and that ain't too bad.