Extensions are 100% eligible for tourist visas and exempt entry's (from eligible countrys). There's no legal basis for denying an extension as long as you haven't broken the law.
Vietnam has a visa on arrival for most nationalities, including US passport holders. You need a "letter of invitation" from any agency (costs $10-$50 depending on speed) and when you arrive at the airport you buy a visa. They only accept USD.
Evisa and the visa on arrival are 2 different things. The Evisa is a proper tourist visa, not a pre approval for a visa on arrival.
It takes 3 business days from when you apply. You'll get an email when it's approved, you need to print it out for the airline (immigration doesn't need a print out though, as the visa is in their system with your passport number). When you fly in, just go to the immigration desk and get stamped in. It works really well. Only reason to use the visa on arrival is if you don't have enough time to apply for the evisa.