I haven't done the e-visa but theoretically it will be digitally connected to your passport but printing out the pdf would be sensible and the double check they have stamped you in correctly on entry at immigration (which one should do regardless of the visa they have as mistakes sometime get made with the date stamp)
as the visa is valid for several months for entry many don't actually have proper flights booked and won't unless they know they have the visa. You just need a confirmed flight itinerary and those can be purchased online for about $15
in that case can't you leave Thailand and then apply for an e-visa? I know you're meant to apply in home country but if you use a VPN I can't see why there should be an issue?