We have arranged a reservation at the Le Jules Verne Restaurant, which is on the 2nd floor of the Eiffel Tower, and is accessed by private elevator. Is there a method of purchasing tickets that would allow access to the elevator that goes to the Summit from there?
There is direct access from the restaurant to the second level. Believe once you leave can't return. At second level tickets to the top can be purchased at the ticket booth, if available.
From Jules Verne, you can access and return from the 2nd floor. However, if you want to take the elevator to the summit, you must purchase summit tickets before going to the restaurant, either online or at the ground level ticket booths (which usually have a very long line).
when you arrive go to the line for tickets to walk up to the second floor and buy that with an add on ticket for the elevator to the summit. Go to the restaurant on the bespoke elevator, enjoy lunch, exit to the second level and look around then use your add on summit ticket to go to the top. There is no way to get such a ticket on the second floor nor can you book only that ticket,but I think this is probably the cheapest work around to do what you want to do. There is always a chance if it is crowded that they won't sell you the elevator ticket in which case, you just don't buy the walk up and proceed. Good luck. Report back how this went.
The line for walking up tickets is much shorter than the line for tickets for the elevators.