My impression is that most compressors are designed to be fairly transparent. So you only get a "fatter" tone with relatively extreme settings, which isn't ideal because such settings tend to introduce artifacts (clicking, etc.) and noise.
It sounds like you are planning to use the compressor as more of an "effect" than as an actual compressor. In that case, you might want to consider a cheap mic preamp, like the ART Tube MP. My friends who run a professional music studio use them specifically to record bass when they're after a thunky/lo-fi/Motown kind of vibe.
I've got one of these...
I essentially use it as an overdrive type of effect. Like your Glockenklang, my PJB rig is pretty dry sounding. The mic preamp blunts the attack a bit and softens the lows and highs, which makes the mids pop out a bit more. You can also dial in a touch of overdrive. All in all, it makes a modern hi-fi rig sound a bit more old school.
That may be right for you. Best of all, they're cheap: I think the Tube MP sells new for under $50.