I don’t think you are going to find a receiver that will do an actual 150 RMS / channel. You -MIGHT- be able to get one that will do 140 RMS / channel, but only if the two LEFT/RIGHT channels are used (the Integra DRX-R1 indicates 140/channel, but I would guess it’s in 2-channel mode -- and this is a very hefty 50lb receiver). If you are using multiple channels (such as 5, 7, or 9+), then the RMS/channel is going to be much less (maybe in the 50-70 watts per channel area). It doesn’t matter what the specs say because many receiver manufacturers do not give fully accurate specs, or the specs are only with 2 channels driven. The power supplies in the receivers are just not enough to give you full 150 RMS/channel.
A true 150-200 RMS/channel amplifier is going to be in the 60-80 lb. area. You just need that much in transformer and power supply.
The one exception here, possibly, is if you find a receiver that uses Class D amplification. Sound quality is going to be different than normal Class AB, and it depends on the type of Class D circuits used.
If you really want that much RMS/Channel, I would look at something like a used Marantz AV7702 processor with a multi-channel amp. There are many 5 channel amplifiers that will do 150-200 RMS/channel for $1000-1500 on audiogon. The 7702 is going for $800-1200 used.
Or get a cheaper Dolby Atmos receiver with a 5-channel amp. The receiver will power the ceiling/back speakers and your 5 channel amp will power the main front/surround speakers.