DWG files are proprietary binary files, and therefore much more difficult to parse and extract data.
DXF files are readable ASCII and these are thus relatively easy to parse [ but please don't underestimate the complexity of doing even this ]...
BUT, someone providing a DWG can just as easily provide an exact duplicate DXF version.
Depending on their software, it's either a 'save_as' or 'export' option...
If you 'colleagues' are not as helpful as one might expect of them ! then there are also several converters to help you...
But some are for $$$...
https://client.autocad360.com/
http://askubuntu.com/questions/49100/how-do-i-convert-dwg-to-dxf-with-free-software
http://anydwg.com/dwg-dxf/
http://www.autodwg.com/dwg_dxf_converter/
Do some investigations...
This newer tool [ http://sketchucation.com/pluginstore?pln=importDXFtextLabel - with floating 2d text labels ] and its formally recognized 'progenitor' [ my tool - with 3d-text - http://sketchucation.com/pluginstore?pln=importDXFtext ] both need DXF files to import the text.
Since these are both 'free' plugins, then you are extremely unlikely to get an unpaid "order of magnitude" improvement in their functionality - especially because you'd just like it to be so, it doesn't make it easy/possible/likely...
If it were so easy to do, then perhaps the authors would have already given you this capability...
Or perhaps offered a paid option for the more involved solution...