I don't quite get your reasoning here:
> if someone has spent an hour of their time (I don't care if it's on company time) to potentially change my life, the least I could do is take 5 minutes to share a sincere Thank You.
That implies that choosing a slower method of communicating somehow shows greater thanks than would, say, an email or phone call. I suppose to some people (certainly not me), a snail mail letter may seem more personal or professional than an email, but I don't think the mere fact that your message arrives via snail mail vs. email would reliably earn you points with those in charge of hiring.