Comfy lightweight bass but sounds bad!

[toneseeker]

Hey Ya'll,
I'm looking for suggestions to make a cheap lightweight short scale p-bass copy sound more thumpy. It's real comfy and looks great so I keep trying to make it work for me even though it currently sounds kind of thin and snappy and sometimes kind of honkey or howly. It sounds very good to me unplugged.
I've tried flatwounds, foam under the strings by the bridge, high mass bridge, felt on the bridge saddles, SPB-3 QP PU's, and I EQ the piss out of it. It's heading in the right direction, but still not there yet. Any suggestions or am I beating a dead horse?
I mostly play country and R&B so I go for the thumpy in the pocket sound. I have other basses that fit the bill, but I keep trying to work with this one because it's so light.

 

[SpamBot]

What amp?

 

[Hilton Marsh]

If you are on a budget then it might be a tough road ahead.
If not then try this.
Replace the pickups with a Seymour Duncan Quarter Pounder. Change the strings to Snarling Dogs and add an Aphex Bass Exciter pedal to your rig.
I made those changes to a Geddy Lee Fender Jazz and it thumps along.

 

[toneseeker]

Thanks for the input so far. I had a 72 J bass that the Geddy Lee was based on and used to play thru heavy 15" cabs with GK heads. Now I use short scale basses and mostly combo amps, but I have tried this thru a 550 watt head and 2x15 cabinet. I probably should just ditch this bass, but I'm stubborn and would really love to make it into another light weight little thumper.
P.S. I've tried the Quarter Pounders, but not the Snarling Dogs or Aphex.