Can you heat an entire house with wall-mounted gas heaters?
If it were me I would investigate the ability to use the existing boiler to heat the entire house. You said that the boiler is reaching the end of it's useful life; please explain why you think so. Hot water boilers can last as many as 100 years. At that age they are not usually very efficient but they will still heat a home or building. With a useable boiler you have many options to extend the  heating system into the unheated rooms. Using unvented heaters as you mentioned is not a good option. You will have the smell, the excess humidity, running new gas lines to each one, the depletion of breathable oxygen and other things to consider. I would never use one of those heaters in a confined space or room. They are cheap for a reason. Go find a good boiler guy and investigate your options using the old boiler. my 2 cents