I've looked at this again. Some time ago I wrote some thoughts on inequalities in this paper doi:10.1080/0020739X.2014.941424
Your problem has multiple variables, which I've not implemented as part of STACK yet. Note, the underlying Maxima libraries for solving inequalities are not that advanced either in this area. I think that problem is rather subtle. As you point out, the case m=0 needs care. Indeed, try your problem on Wolfram alpha and have a look at the result.
In the past I've started from the educational and CAS aspects of the problem and used these to inform the development of STACK. The above paper is an example for single variable inequalities. This is something similar for scientific units: doi:10.1088/1361-6404/aa5e9d
We probably need something similar for multi-variable inequality problems as well. This isn't going to make version 4.2 this summer. Sorry.