Hudson is right - the best way to manage this is to create a CGM then import back to UG before doing your DXF translation. I would add that when making the CGM, be sure to use "TEXT" instead of "POLYLINES". That may seem really obvious to some, but it's bitten me when I was in a hurry.
The problem you are having has to do with what you call "automatic text." DXF doesn't recognize the expressions used for text that is automatically updated by a UG file. Partially because command lines vary between CAD tools, i.e. what works in UG doesn't necessarily work in PROE, two different products, two different results. Expressions are tricky animals that way. You shouldn't expect a translator to pick up anything that is not a solid value, be it text or any other part of your CAD file.
Besides all of that the expressions you listed are not common to UG. Those are obviously site-specific attributes created to make drawing creation more time effective. In other words, my UG wouldn't read that "automatic text" any better than a DXF. The block would appear to be blank, but a text placement would be there. I'd have to change the expression to a value, or add the attribute to my drawing.
If you have AutoCad and are able look at your DWF post-process, check to see if there is a blank piece of text in the block. I don't know AutoSad very well, but I suspect that you may find there is text there, but the system can't read the expression.