Can my employer force me to provide a post-dated check before I leave the company in order to repay a tuition reimbursement?

1) No, they cannot physically restrain you from leaving *any time* you want: the most they could do for you leaving earlier than they'd like is fire you, after all. If they try to physically restrain you, lock the doors on you, etc.,  call the police and press charges for unlawful restraint.
2) They can't withhold or debit your final paycheck, even if they believe you owe them money (e.g. for tuition reimbursement) but refuse to provide them a post-dated check: if they do, you can file a complaint with the state department of labor and/or sue them for the final pay withheldor debited. You may be entitled to additional compensation for their unlawful withholding/debiting. The law is very clear that employee pay can only be withheld with consent (e.g. if you agree to let them take repayment out of it) or by court or IRS order (e.g. wage garnishment for child support or taxes).
3) Therefore, they can't force you to provide a post-dated check before you leave: you can just leave when you want, and they can't restrain you or keep your pay.
4) They are allowed to nag at you, remonstrate at you, and generally complain about you leaving without providing the check, but that's all they can do: you can simply ignore them.
5) They *can* sue you if they believe you owe them money for tuition reimbursement--that's what you do when you think someone owes you money: sue. But to win, they'd have to prove that either there was an agreement that you'd repay the tuition under these circumstances or that you committed fraud (e.g. lied about you intentions; such as claiming that you'd keep working there to get them to cut the tuition check, then gave notice as soon as you got the benefit) to get them to pay for your tuition. Without an agreement to repay or fraud committed by you, you are not obligated to repay.
6) There is no general "employment record" for them to put a black mark on. IF a prospective or new employer calls them for a reference, they can say anything negative about you which a) is the truth or b) is simply an opinion (since anyone may have and state any opinion): so they could say that you received tuition reimbursement from them, then refused to repay it when you left work, if that is true; or that they consider you untrustworthy or ungrateful, which is an opinion. But if they say something which is provably false, you could sue them for defamation.