In theory, if you receive a project who’s TM is in TRADOS 7 you should be able to export the TM into an earlier version of TRADOS, i.e. 6.5 by simply telling it to. Now, what you would then have to do is take the export files, go to TRADOS 6.5, create a new TM with your languages, then import what you exported from 7 into 6.5 and work from there.
Then to get the project TM back into TRADOS 7. You would export the TM from 6.5 and import it into 7. I don’t know if this will work but there is a possibility.
You don't have to perform the last step. Once you've back-converted your TM to Trados 6.x, this can be read by all Trados versions. Trados 7 and above support opening the legacy .TMW format seamlessly!
The rest of your description is correct, that's what I do too when I have to send a 7.x TM to a translator running 6.x.