
How I know what you mean about the extra running to catch them!
My old rescue boy that we lost in December was deaf. He was also partially sighted, so couldn't actually see me waving further away than about 20 feet! If he 'lost' us, he would ALWAYS choose to go in the opposite direction. I had got my young shepherd about a year after adopting him, and trained her to 'round him up', which she always did brilliantly. The only trouble was she would circle him at such a speed and race back to me that sometimes he missed it :D
My very first dog went deaf in old age, and Red, mentioned above was totally deaf when we adopted him. I wouldn't hesitate to have another deaf dog, good on you. There are of course the little advantages - no barking at the post arriving, no hassle when opening a crisp packet (if they're not looking) :D
I think the coat idea is a fantastic one, If you bought a normal coat you could take it into one of these places that personalises T shirts and get it done for you. Perhaps you could take the message one stage further, and say 'if I'm following you, please wait' That's what I found was the worst, Red would follow a pair of legs, and often they just kept walking and he was as happy as larry thinking he was with me - bless! He's gone now to a place where I hope he can see for miles, and hear a pin drop!
Kat