First of all you need to be clear on what your looking for,from your description of things i think you have the terminology confused.
A PREAMPLIFIER takes the signal from the source,cd player,dvd,tape ect & sends it to the amplifier,it also gives you volume control,source switching & depending on the make & model tone controls & loudness,balance control too.
A PROCESSOR can be used as a preamp but its main functions are home theater setttings & not stereo functions,rarely do these units contain standard tone controls as in actual knobs that you can adjust,instead they use equlization programs & bass management settings.
A PRE/PRO is a combination of a stereo preamp with a HT processor,some of the more expensive models will have seperate tone control knobs for bass & trebble but most do not.
An AMPLIFIER
only amplifies the signal,amplifiers do not have tone controls or loudness contour,some amplifiers will have whats called "gain controls" that act like volume knobs but most do not.
An INTERGRATED amplifier is a preamp & amp put together in one chasis,an intergrated will handel all the source switching between components like tape,cd,dvd ect,most intergrated amplifiers will have tone & loudness controls & all will have volume controls.
A STEREO RECEIVER is an intergrated amplifier with a built in tuner so you can listen to the radio,stereo receivers will have bass,trebble,balance & loudness controls as well as a few other features.
An AVR (audio video receiver) is all of the above,these units contain a multi channel amplifier,a preamp,a processor & a tuner,most AVR's do not have standard tone controls as they are useless for the design of the unit.
Bass takes power plain & simple,you need wattage to properly run a full range signal from 20hz to 20khz,a full range speaker that is not reinforced with a powered (active) subwoofer will drain the power "wattage" of most economy model AVR'S.
Some of the more expensive model's of avr's have powerfull built in amplifiers but most economy models do not,they do not need powerfull amps,the use of built in crossovers inside AVR's will send most of the heavy bass to a
POWERED SUBWOOFER,powered subs have their own built in amplifier so the built in amp in the AVR is handeling the easiest part of the load & the amp in the subwoofer is handeling all the heavy work load.
Now to decide on what you need,if your current AVR or RECEIVER does not have the tone & loudness controls you need then sell it off,you have lots of different directions that you can go,an equlizer is not the right direction for most people who are new to this or who want a simple system to operate.
Your current receiver is not only lacking tone & loudness controls its extremely underpowered,Cerwin Vegas like power,even though they are pretty easy to drive they still need alot of power to sound their best & to deleiver the bass they were intended to,adding an equlizer to your current receiver will not only complicate your system it will heavily tax the underpowered amp in the reciever.
For killer bass at loud listening levels you should not rely on using the loudness feature,loudness is supposed to be used at very low volumes due to the extreme boost in bass response,for loud volumes you should use tone controls only,this is where a hi powered amplifier comes into play.
Your best & most economical approach would be to buy a pro amplifier & a stereo preamplifier,for an amplifier the
BehringerA500would be perfect for your power needs & fit your budget,it costs around $200.
For a preamp your best bet is to buy a used model from
Audiogon.com,Audiogon is a site like ebay but its main focus is 2 channel audio gear,here is an excellent example of hi end preamps that sound excellent at budget prices,this preamp is a steal.
http://cls.audiogon.com/cgi-bin/cls.pl?preatran&1185312757
With the cost of buying a new Behringer A500 amplifier plus the cost of this NAD stereo preamp,plus shipping your total cost would be right around $400 & this combination will work & sound better for your needs than any $550 receiver you can find.