I will try the hair dryer first to see if it has any effect. If not may try the heat gun, depends on how heat works. I do have a messy fall back plan. I used one of the orange cleaner products when I first started but only used a cloth, not a brush. It totally dissolved the black stuff as well as the finish on the floor. I do not know what finish is on the floor because the new carpet has been down since 1999. It replaced shag carpet from the 60's or 70's and the block tile was under that. The block tile must have been down since the 40's. I doubt they had poly then so it is probably just wax. I have been told that the orange cleaner will dissolve all types of glue and related products, but I do not know how much mess it will cause.

You may want to try some of this on your cabinets. It is biodegradable and not hazardous to breath. I know it dissolves wax but I do not know about a cabinet finish. I just used a sander on my cabinets when I refinished them.