One thing in your letter is wrong.

I never went to the hospital with yellow fever; some of the men had it aboard ship, and I took one of them to the ward the night I ran away.
The doctor at the hospital wanted my name, and I gave it, and this may have been how they thought it was me, but I did not intend to deceive you or anybody else, nor cover up any tracks.

Yes, father, I'm coming home.

If you'll hold out your hand to me I'll take it gladly.

I've had a hard time since I left you; you'd forgive me if you knew how hard it has been.