Using a Multiple Load dimmer to it's full rating?
The 1000 watt version of the Lutron dimmer you mentioned in the question is the best solution.

https://www.amazon.com/dp/B000MASMU8/ref=cm_sw_r_cp_api_2M1gAbZC0JPCV

You're correct that 600 watts on a 600 watt dimmer never lasts.  My personal theory on that is that in a perfect world input voltage would be the rated 120v.  In the house, in the real world, voltage could be 10% or more lower, which changes every other variable and effectively increases current draw slightly.