How can I get a closer shave?

I have very heavy/coarse facial hair, and try as I may, I can’t ever get a close shave. I’ve used hot towels, any assortment of fancy schmancy razors, pricey shave gels, various facial gymnastics while shaving..and other products/techniques advocated by the likes of GQ and Esquire. However, short of using a blowtorch, the best I can do is get to “sandpaper face”. Fellas, help me out.