While I certainly understand why you are asking for all of these things, I am not sure that all attributes are going to be supportable. For example, for the total noise to be equal to 1mm/s^2, with a bandwidth of 1.5kHz, the noise density needs to be 2ug/sqrt(Hz), which is substantially (~50x) lower than what is available in all of "tiny" MEMS accelerometers on the market that support this type of bandwidth.
ND = (1mm/s^2) x 1g/(9800mm/s^2) x (1/sqrt(1500x1.6)) = 2ug/sqrt-Hz.
Assuming some relief might be available in the noise, the ADXL350 or ADXL203 would be the products that I would start with. I hope that helps!