Glenn, your suggestion of contact cement for veneering was spot on! After using wood glue on the White, I contemplated using it again when a Singer 66 treadle came my way. The top wasn't horrid but wasn't going to be an easy clean up.
Used a scraper and heat gun to loosen and remove the old battered oak top, that took less than 10 minutes. Then from prep to placement of veneer was about 30 minutes. Five minutes of that was looking for the cement! A good rollering and today it is being trimmed, sanded, and stained. SOO much easier! I used a cheap chip brush to put the goo on and then tossed it. No clean up. Thanks!