Scragging is the proper term for taking a steel road spring beyond its elastic limit, in order to set its free length and possibly do something to residual stresses. By extension we use the term when testing bushes - before testing them we always exercise them for a defined number of cycles at a high load.
Typically after 10 cycles the hysteresis loop has only 1/3 the area of the first cycle.
2000 pa is not enough to justify a fancy rubber bush, I suspect, so I'd forget my hydrobush idea. Your estimated cost for a rubber bush is about right, for one perhpas 30-40 mm on its longest dimension. What duty cycle and life do you need?
That temperature range is fine. I strongly suggest that you talk to a rubber bush manufacturer when designing the part he will be able to guide the design. We often work from a known similar part, test it, and then juggle the geometry to get the desired rates.
Another form of cheap damping is to use foam pads to create friction.
Cheers
Greg Locock