Chess, it's like Home Center bath cabinets. Veneered edging, no matter pre-glued, or glued by you, is so thin (1/32" or less) that it doesn't do well with changes---ANY, like temp., hum., heat, direct sun, water, ice, etc. Could you edge it w/ 1/4" (or a bit less) strips of a weather-resistant hardwood instead? Glued, clamped and set-screwed? Stain/finish as desired?

Always call the place you live a house. When you're old, everyone else will call it a home.