I got curious enough to email our registration authority and ask if a non-EU citizen, non-resident can purchase a motor vehicle here if they have a local resident to name as an Authorized User. Nothing I could find in the laws says they can't. Not necessarily relevant for you, but it's an interesting question.

EDIT: Just received an explicit answer from the Maanteeamet (vehicle registration authority). Yes, a non-resident, non-EU citizen can purchase a vehicle in Estonia and register it in their name if they also have a local resident to put on the registration as a representative/authorized user.

Hi,

Do not know exactly the answers to your question about leaving without the bike and special inspection. I live here and have never brought a foreign number plated bike here. I am ok to try to find out but it's too early now.
Your departure is planned next summer so will take clearly over a year, if at all, you will arrive here. Regulations and parking solutions can change in the meantime. If closer to date your plan is more concrete, please reach out to me again, happy to help.

Wow, that's really useful information, thanks AnTyx for taking the time to post it, much appreciated

Thank Marcel