Since I am old hardware EE kinda guy I tend to think of solutions that don’t involve software. So if you were willing to canabalize an sdr by breaking into a LO signal or just the base oscillator , set up a mixer, then mix audio frequencies with the original signal you could achieve a slight shift based on the frequency of that audio signal you apply to that mixer. Better yet, get your on VCO that has tight controls and use it instead of the LO. I am assuming that you can get to it. Some of those cheap dongles might be more forgiving of the hacking although you’d need an upconverter.
You might find some other ideas by visiting this site where you might find links to devices that these guys use to participate in these frequency tests.
Just to satisfy my curiosity why are you wanting to do this? Are you thinking that some of these MW stations are operating outside established spec limits? So then you could get with them to help them make corrections?