Your LP is your bed and you are going to do 9.2
And the .2 are 18 inches
Assuming a bedroom this is a lot of bass
I will try to answer your questions to the best of my knowledge, and my ability to pass it on, many time I express myself the wrong way
For "What would you suggest for a real processor and amp(s) if my budget for both is $2000? What would a real processor gain me? (Actual, serious question)"
This last one, I have to be conscious not to steer in the wrong direction since it is not my money!!!
The way of up grades to be heard as to biggest improvement to the least are;
-Speaker and sub/s first and room acoustic.
Both can play a big difference in your sound, so both are equal.
-Power, either from a receiver or power amp, if the power source ran out of juice, you will run into distortion and worst, clipping, a very dangerous place to be for speaker, since clipping can damage speakers. This is where a power amp make a difference for the power.
-adequate electronics and cables, speakers wires and cables should be of the proper sizes and I am guilty to over size when not needed.
How many channels do you need for a power/s amps?
This would be my second upgrade if you do not have room treatments.
Last but the most important one for the budget.
The processor fall into electronics. This one is difficult to explain and will try to do my best.
Processor use better parts;
DAC (Digital to Analog Converter)
Resistors, capacitors and so on.
At the end, it result into a more spacious sound that make the speakers disappear.
My most important suggestion to you.
Buy an AVR for now!
The words of electronics is moving to fast for the formats wars.
2 years ago, my processor was a reference piece, now it is a boat anchors.
When all the format settle, then you can move into processors if you still so desire