You'll go through a lot of different emotions over the next months. Take the time you need, grieve in your own way - there is no right or wrong here. I re read your post and noticed you said
I can't help but feel like I came up short. Maybe that's just a natural feeling, I don't know.
It is natural. I makes sense. Regrets for doing this or not doing that better is all part of the grief. It's a common thought.
I don't know you at all and I don't know if we've even talked before....but from your letter you sound like a really good son.
You will be in my thoughts and prayers.