In my experience, I would like to suggest a few things. You definitely got some things right as far as your approach and assumptions: yes, a physical address is definitely a must - PO box is not advisable for the reason you stated. If you don't want to use your home address, get a virtual office (through a co-working community in your area or a UPS store, where you can rent a mailbox.)
Also about the envelope: I write my personal name with a physical address as the return address. As far as the addressee, I put first name and last name of the person, and if there is a spouse, I am very careful about including both names: people get "offended" if you omit one of them, I know I do :) I try to get an interesting stamp, not the generic 'forever' stamp. Also I put a tag line on the envelope underneath the return address, like 'bail out plans available', 'cash for your equity - any condition.' They get more envelopes open.
Don't worry about a website - more important is establishing an internet presence in social media, especially Linkedin. People will "google you" and an internet presence has more weight than an unknown website.
The letter should be brief - the main point you want to come across is that you are here to give them solutions, help. It is about them, not you. They don't care you have closed on hundreds of deals and you have a big company. They want to know that you are the person helping them out of a sticky situation and that they get some money out of the deal. Always give them money - even a short sale, squeeze out a couple of thousands for their moving expenses, etc. and state that in the letter.
All my letters and envelopes are printed - I don't handwrite anything, to me it is unprofessional. I think how I would feel - it is a little "scammy" to me to receive a handwritten letter, when I don't know the sender and I am being made believe otherwise just to open. May be that is just me, but I have had good success doing things as stated above for over 20 years, so I guess it worked ;)
Good luck!