Expecting gain out of an active filter is tricky, because you need GBW sufficient to include the filter's behavior, plus the gain, and this very quickly limits your performance. A 4th order Butterworth filter might need a Q factor of 3ish in one stage, which means GBW roughly that many times the cutoff frequency. Which means, for 12MHz op-amps, you are limited to a gain of 40 in that stage. (Which is still not unreasonable, but you should allow some headroom to keep distortion down, and the bandwidth accurate.)
If you could tell us more about your signal source and its nature, maybe a better suited system design could be considered. Is the signal always exactly ~2mV? Does the midband gain really have to be exactly 1000? Would a cheaper gain stage using discrete transistors be overall better? Would a variable gain stage (the equivalent of radio AGC) be desirable?
It's best to have a chunk of low-noise gain out in front, to raise your signal level above the noise level of the remaining signal chain. Then you can apply whatever filtering and amplification is necessary, without having to worry about noise (which will be a modest concern for ~2mV signal levels, in this bandwidth).
Point being, you don't need a 10-100kHz bandpass on each stage. The bandwidth limiting only matters to the stages where excess bandwidth is a problem: the first stage probably doesn't mind, because the signal is so small. But if there are strong interfering signals around, they need to be filtered away, or even the first stage can be driven into clipping. (To account for RFI, a modest CLC filter might be used, with a cutoff frequency of ~MHz. It won't affect the desired signal bandwidth, but it will do a damn good job preventing interference.) The bandwidth probably should be kept within the desired range before the final gain/output stage, because it's close to clipping, just from the signal alone.
Oh, and note that an oscilloscope with 10x probes will have basically no reading for ~2mV signals, while your circuit will be slamming into the rails at the output. Just because you can't see it on your instrumentation, doesn't mean the circuit isn't seeing it! That's really what's meant by "scope the rails": measure it to a degree satisfactory to your circuit's sensitivity.
Tim