I understand this is all instinctual. He's a mastiff mix and he isn't cut. The big issue is it makes his hormones go crazy and he ends up bleeding (spotting, really) from his man biz. It also makes him mount our other male dog and act "aggressive" toward other dogs. When he doesn't lick, probably when the neighbors lady dogs aren't in heat, he does fine. No bleeding, never mounting the other dog, very friendly to other dogs, then he gets a lick and he's dominant and stupid all the sudden. How do I get him to stop?
Dominant or mating behavior doesn't involve any bleeding in males. You should get him checked by a vet (preferably when this bleeding is showing up). He might be in pain, maybe from urinary stones or some infection. Pain can make dogs agressive.
To rule out any infections or deficiencies, the vet should make a blood test.
Apart from that, if your assumption that this behavior is caused by female dogs in heat is correct, your dog seems to show very strong reactions to female hormones. If there is no other physical cause for his behavior, please consider neutering him. Raging hormones can mean a lot of stress for a dog. He won't hate you or be "less of a man", but more of a relaxed dog afterwards. The issues you describe won't be gone all of sudden. It's your responsibility to train and exercize your dog in order to balance his need for action (like running, playing) and rest.
In any case, you should consult a vet regarding his general health and hormone levels.