Hey Iota,
I am not sure if my experience can help, but I've run into similar problems and after years of gear searching and playing with my EQ am only recently (the last month or so) really honing in on a tone that I can live with.
My guess is that it may be your amp more than your basses, but after spending ALOT of time, those GK's can be pretty sweet.
I do not have the MB212, but I have the MB210 and am familiar with the platform. For basses, I use a modern sounding MTD and a passive Godin P/J. With either bass my GK is naturally hi-fi sounding and offers difficulty when trying to coax smoother tones out of it. I am not home to look right now, but for me, I am finding it best to leave my onboard EQ flat and on the amp I am near flat, but with a nice boost in the low mids, cut on the lows and slight cut of highs. The longer I own the GK, the less I find the need to cut lows as drastically.
That gives a nice, super modern ton which I love, but is very distinct and not very versatile.
For me, the answer has been the Tech 21 VT Bass (I have the deluxe, but the newer non deluxes have an amp simulator defeat switch, which I am not sure is necessary). I have been fighting the urge to use it with my GK, or my SWR because of the time I spent to find plug and play equipment; but the fact of the matter is, it really enhances my tone no matter what I am playing through and allows me cop close to any tone that I currently need.
You could look at other basses, but I've heard the Bongo crush it in gospel. I am also of the belief that a P-bass can cut it with evened lows and heavily boosted mids. If you do go with another bass, make sure you try a similar one with a similar GK MB. Every bass I have played through an MB sounds dramatically different than it would through any other amp.
If you are interested, I can take some shots of my set up later this week. I could probably do clips to, but am not sure that I will have the time.