I agree with Shady and TLS Guy. To summarize, you pushed your system too hard because:
1. The speakers are not designed for the kind of spl you need. This is an educated guess only, without knowing your room dimensions, amount of acoustic damping, sitting distance, and to certain extent the media contents you have been mainly listening to (types of movies, music etc.).
If you don't want to provide the into, you can use the online calculator linked below and let us know the results. It won't be very accurate but should be good enough to help troubleshooting.
http://myhometheater.homestead.com/splcalculator.html
2. The RMB1585 has relatively
low input sensitivity, 1.9V RCA, 3.8V XLR. The Marantz could therefore be clipping during certain peaks in the media contents you listened to. That would of course result in the Rotel clipping as well.
3. It is hard to know for sure without knowing whether you ran Audyssey and have it on all the time, and the level settings after running Audyssey, but it seems very likely that you are listening at or exceeded "reference" level from your main mic position. For Marantz, the volume scale is 0-98 or -79.5 to +18, so 80 is about "0", and if you had ran Audyssey correctly, that would represent "reference" level (THX standard) at your mic position, and that would likely be too loud for most people.
Note: When you get the speakers fixed, at least temporarily, you may be safer to just drive the speakers with the Marantz SR8012, for most movies and 2 channel jazz/classical music and only use the Rotel for compressed music listening. Do make sure the Marantz SR8012 is kept cool, with an external fan if necessary. Obviously it will help a lot if you can turn the volume down a little, instead of 80-83, try 73 to 76, or if you drive them directly with the SR8012, you could try 75 to 77 but do check for temperature.
If you like those speakers, and they are really nice sounding ones, then you may want to consider changing the crossover settings to 80 Hz, preferably 90 Hz, sell the RMB 1585 and get a 3 channel amp such as the Halo A31, or Anthem MCA 225 that has higher input sensitivity. Note: setting the crossover point higher than 80 Hz should help, but not very much because the speaker's impedance hoovers around 3 to 4 ohms between 80 and 200 Hz. Phase angle looks good, and the Rotel amp can take the heat anyway, it is just the impedance we have to be careful with.