Of course, bathe right before going to work. Hopefully, you can keep cool before and during work. Antiperspirants are not a good idea anytime, but especially during the MC, because you are blocking one of the ways the body eliminates toxins.
Depending on how long your shifts are, you might have to wash your armpits often (I had to do it about every 6 hours at the height of my MC). At least bring some fragrance-free, alcohol-free baby wipes with you and rinse it (the residue) off with water. Powder yourself with cornstarch. When you are off duty, sweat as much as you can with exercise, saunas, swimming, long baths. Your skin is one of the best ways to get the toxins out and the quicker they are out, the quicker you are off the MC. Don't forget, DRINK LOTS of WATER!!!
I tolerated the bad breath and brushed often, but I heard about people gargling with liquid chlorophyll (from healthfood store).
Don't use mouthwash (chemicals) or gum. If you haven't already, switch to a healthy toothpaste made of plant oils (and no fluoride or saccarine). I also learned during my last week that you can rub off that coating on the tongue with a flat cotton ball disc. I never got any off with brushing or those scrapers. Rubbing off that coating could help open those passageways to get the toxins out quicker and probably remove a source of the bad breath.