First of all, sorry for your loss. I waited to see some of your reactions to the suggestions before giving you my input. I'll start with your wrist size, even if someone else have the same size, it doesn't mean it's the same shape, some are rounder, some are flatter; only you can tell what is the best size for you, and you already said that ~38mm is ideal for you, so let's stick to it.
IMO, a vintage watch, or a used watch is not an ideal way to mark a milestone in life, and I, personally, don't see the point of buying a watch that was worn by someone else the day that I was born; best case scenario, he was chilling in front of his TV, worst case scenario, he was comitting a crime.
That is settled, and you didn't express an interest in any other Omega, so, let's drop Omega.
Now, you are comparing your favorite watch to classic Rolex models, not to Tudor, or Omega models.
Ok, you never spent more than $400 on a watch, and this is going to be your first substential spending on a watch, and it will mark two major milestones in your life, so we'd better get it right. Your budget is $3K - $5K, let's see if we can find the perfect watch that can live up to your expectations.
Here, we have a suggestion for an OP 36, and others suggested OP 34 and OP 39; different sizes, but same watch, same spirit, the pure beauty of a Rolex in all it's simplicity. Not only you can find the pefect fit for your wrist, and the perfect color for your taste, it fits in the budget you already set.
And I agree with you! Judging by your reaction to this picture, I can only imagine your reaction when you'll try it on your wrist. Hope it helped, Good Luck.