That's correct. If you don't need to show your transfer as being international you're better to select Living Expenses as the payment will be routed through the most accessible bank and will (usually) be faster
The Long Stay option will often take longer because it's the one which gets noted as an international transfer so Wise has to ensure it goes directly into Bangkok Bank or Kasikorn Bank (whichever you nominate) and not through an intermediary bank. This process always adds a bit of time. I did one yesterday at 15:00 and it was deposited into my BB account at 10:00 this morning, so almost 24 hours
Since when has immigration preferred agents? (Other than the fact that they're getting bribed). I've been in Thailand 15:years, never used an agent, never had a problem with immigration