Yes, the fact that the Open Sleeper ticket is one of the very few remaining ticket types that remains a paper "value" ticket and not an eticket makes them a pain. I just looked at Cincinnati station services and, while it showed checked baggage service, it shows the ticket office closed, which is odd. When there were more paper value tickets (international journeys on the Maple Leaf, the USA rail pass, many Thruway buses all required them long after the general move to etickets, but those are all now etickets), Amtrak always offered a mail option if the travel dates were more than 7 or 14 days away (I don't recall the exact time period). I am surprised they do not still, especially given how they have cut back on agents.

I have to say if I were you, I would take some defensive actions and not just arrive at Cincinnati hoping that you will be able to pick up that ticket, given that the website says the ticket office there is closed and there are no QuikTrak kiosks, either. Call during East Coast business hours and once you get through to a agent, ask to be connected to Customer Relations (who are only there normal business hours East Coast time). They are the most empowered customer people in the company and are the the likeliest people to be both able and disposed to help. Use the AGR or Select phone numbers if you can to cut through the initial wait, which is horrendous right now. Of course, if the journey is less than about two weeks away, to give time to have the ticket mailed, you are out of luck, although Customer Relations ought to be able to give you a definitive answer on the ticket situation at Cincinnati. You need the physical ticket for Open Sleeper, there is no electronic version to transmit. If the trip is close, your only safe option may be to go the nearest known ticket office, which is probably Indianapolis. In days past, when value tickets were the norm, it was not unknown for a last minute ticket purchased for an unstaffed station for the ticket to be sent out with the conductor from a staffed point. But I suspect that practice is long gone.

Luckily, when I had trips that involved paper value tickets (Open Sleeper once, several trips on the Maple Leaf), I was using stations that had and still have ticket agents, so all I had to do was arrive early enough to allow time to pick them up.