If it makes you feel better, having the transaction ID wouldn't help. I'm in a similar situation except I do have the original PayPal transaction ID, and when I provided it I was told: "Sorry, our system for looking up transaction IDs is currently unavailable. You'll need to provide alternative proof of ownership. No, the original email address associated with the account isn't good enough. No, we won't tell you what is good enough."
Tried again a year later and got exactly the same response.
Tried again a year later and got exactly the same response.