I didnt observe that your previous 797 is valid and the new 797 is not going to start its validity at the time of your intended stamping appointment date. Yes, you are right, you should present both of the 797 copies for stamping. I would suggest you to write a covering letter requesting your stamping validity to the validity end date of new approval and attach the copies of both 797s under that letter. Also at the time of interview, you may want to refer this fact of requesting the latest 797 date for visa validity towards the end of the interview. Also once you received the stamped passport, check visa validity end date. If its not as per your new 797, immediately send the passport back to the consulate with a copy of your original request letter that I am referring above along with new 797 copy.
On the other hand, Visa is just an entry permit, the visa end date need not be your I-94 end date at POE. If you are not intending to re-enter into US before the end date of new I-797 end date, it really doesnt matter.