I had a situation a few months ago where I was stuck in DCA due to a mechanical issue and was going to miss my connection to MLB. My options were to get into MLB at 11:30 AM the next morning with DL paying for a hotel at DCA or they could get me to MCO that night at 1AM. I told them I'd rather get into MCO that night but I didn't want to make the 1+ hour drive home that late. The DCA agent didn't hesitate to authorize a hotel at MCO that night after I got in and the MCO agents put me up at the on-site Hyatt without issue. I (or rather my company) took care of the rental car to get back to MLB.

Long story short: DL is usually very liberal with free hotel rooms for MX delays.