Bright, You are desperately trying to find the timeline of when your h began his journey. Unfortunately, you won't be able to narrow it down to a certain time period. I would venture to say that he had been thinking about the drums for a while and who knows, he may have remembered how he when he was a teenager playing them. Sometimes they look for material things that made them happy as youngsters. The memories are what determine which things that they really want to take on their trips to Oz.
As for engraving something on the drums, I wouldn't do it. He already knows that they are from you and that you love him. He doesn't need any reminders of this.
Now, it's time for you to turn your focus back on to you and your job search. You need to focus more on your resume and figure out what needs to be tweaked.
It's time for Bright to live her life to the fullest and allow the man upstairs to take care of your h. Fretting about him and searching for timelines won't make his journey go any faster.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.