I've thought of doing this... either to a wood tv tray or to the top of a rolling printer cart. I didn't want to staple the materials down though. Duck tape... when it gets really hot... melts and lets off toxic fumes. But I should think that it would be fine (if a bit industrial looking... lol) in this application.
For now I have a press mat and a press board that i use on top of various things. I switch out the flat hard press board and a rotary cutting mat on the one surface, depending on what i'm doing. The ironing board only comes off the wall when I've got serious yardage to iron.
Can you fold up your TV tray/ironing board now?