Try checking the name of the actual template document if it's "Customized Reverse Auction". It might be the name of the template workspace itself and not the template document..
Please, check these steps below:
1. Go to Project Template-->Document Tab
2. Select Actions--> Document Choice
3. for Type select Event
4. then choose the event that you have created [remember that here is the document name that is displayed (inside your event project template) and not the name of your event project template, so if they are different maybe it is one of the reason that you aren't seeing it)
Are you trying to replace an existing document choice from the full sourcing project template? Also, can you post screenshots of step 3 and 4 you mentioned in your query?
Thanks for all your help. Now I can able add the event template to Project template.