When you first make designs in MML, ensure the year of your Mech designs are appropriate for the AtB year you're playing. Also note their tech level.
For the MHQ part, check your tech limits to ensure you have "only allow canon units for purchase" unchecked (which I know you've been told already).
Make sure your allowed tech level matches those of your custom designs. Advanced covers most of the era-apporpriate weapons, but you may have Experimental level tech.
You might need to uncheck "Disallow extinct units and parts" if you're trying to, say, shoehorn rocket launchers into 3025. But that might get you some out-of-era market purchases at some point.
In MM itself, under the Allowed Units and Equpiment tab, make sure your game options reflect the current year of your AtB game. Also ensure Canon Units Only is unchecked.