You know, we had a student almost as bad as what you described come to our dojo a few times. Not only did he complain the mat fee was too expensive--he wanted to train about 8 days a month with us, but was part of another dojo and didn't want to officially "join" ours, which is fine, we have a few students like that, but the thing was sometimes he wouldn't pay or would say he didn't have enough money--he even tried to pay $10 for a $55 seminar! He would make all sort of excuses.
He wouldn't take ukemi often, sometimes he'd grapple if a higher ranking student tried to throw him, and being the only girl in our aikido program, he'd follow me around and try really hard to practice with me, even though my creep meter was going straight off the charts (it got so bad that my husband, whose classes he often came to, forbid me to practice with him and had one of our tougher/rougher live in students even interrupt him when he tried to practice with me and pair off with him), telling me about how the love of his life was Chinese so he knows all of our customs and stuff but then she left him, etc. Talk loudly and correct higher rank and lower rank alike, always arrived forty five late (we run an hour and a half classes) so he didn't have to exert himself, talk back to sensei about not doing the technique the way we were doing it because it wasn't how he was taught.
He hasn't come back in a while, because he got told off in front of the class by my husband about his disrespectful behavior (after having multiple private talks with him), and our live in student became in charge of collecting his fees (and the student is a no-BS kind of guy.)
Sometimes, in all honesty, these people will never learn. You have to decide if it's worth keeping him if he's scaring your female students. If they don't feel protected, and they leave, then you lost multiple people to that one person, and it is still a business.
thank you for sharing your story. . I'm not a woman, and my creepy meter goes off. Your problem is very similar to our problem, only our problem guy is very good about paying dues... but we have an automatic payment system.
We had a Shihan visit last year at a seminar,(an 8th dan) our problem guy showed up and took this class like every other class. He was teaching in the class and following beginners around and instructing them. I was severely afraid that our Shihan would notice, it would be such an embarrassment for us. I took the guy aside quickly to remind him not to do this... and for the love of God not in front of our Shihan. He disagreed with the Shihan. He thinks what we do is BS, though he says it in a back-handed way and isn't aggressive with his opinion... but actions speak louder than words. I think you are right, and I don't think this is some one who will every learn from us.