Are there any Mosek warnings after you changed units?
Have you looked at the log? It indicates that your problem almost converged (the primal and dual objectives are very similar), but that the solution has norm of order 1e+14 (primal) and 1e+10 (dual). Getting a reasonable answer when the expected magnitudes of the solution are so huge is unrealistic, I would say that the solver does unexpectedly well given the circumstances.
Your problem is probably borderline infeasible, so that the solution, if any, is extremely far away. Such illposedness is a very hard situation for the solver. There is no good advice rather than restructure the problem so that it either has a solution of reasonable size or is robustly infeasible.
More about evaluating the Mosek solution summary in 8.1 Understanding optimizer log — MOSEK Optimization Toolbox for MATLAB 10.0.43
I am unable to change the parameters because I am running someone’s model according to their paper…