Basically, I have been doing since more than 3 years via tm47.immigration.go.th. I just applied for mine a few days ago and am now waiting for it to get approved. You just need to fill out the information very accurately and submit it at least 10 days in advance. That would be the most suitable time to do it.
I think you need to get those documents. Just visit the Embassy of Nepal in Vietnam, pay the service fee, and obtain the documents. It's not something I'm wondering about.
In case you need additional medical letters or medical care, please let me know. I work at Phyathai 3 International Hospital. We can provide further assistance.