Im not very well known about purchasing bikes in Vietnam but for the rest you seem to be mostly correct. But remember this is SEAsia and enforcing and interpretation of laws and rules changes as often as a normal person changes underwear.
The 90 day visa you talk about for Thailand - thats a Non Immigrant visa and I really dont think you will need that type of visa. A normal tourist visa of 60 days should do. I have even heard of several who bought motorbikes on a visa excemption 30 day stay. But again - this is about interpretation and enforcement of laws and rules. The time one have to wait for documents and new plates in Thailand can vary a lot from province to province, from a couple of weeks to several months.
Entering Laos have become more difficult the last years. From the thai side most borders demand that you are in a group and het permits, and mostly they seem to enforce the old rule that says you need at least a 250 cc bike to be able to enter Laos. Then again not all borders seem to enforce this rule.
Basically renting is so much easier in all of these countries that it must be the better option. No document requirements, no visa requirements, no insurance requirements, no bordercrossing hassles - just rent and go! Its actually a no brainer if you ask me...
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In the end everything will be fine. If its not fine its not the end....
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