Legally you can extend every entry on either Tourist Visa or 30 days visa exempt bu anther 30 days, that should give plenty of time to sort you out. Re ED Visa application, in principle no problem as a first timer, however at the moment it appears there is a backlog, expect not less than 3 weeks processing time. I would avoid Singapore, but ask your school they should know best.
Why you think you will have a problem ? As long as you prepared to pay for Laos visa you are fine. For the Non O at Thai Consulate it should be OK. Your Non O is based on what ?
as this will become another complain topic about the Royal Thai Embassy Vientiane I will close comments. I send them a message asking to issue an Official Announcement about their policy so people not waste time and money.