TGMT - They are unusual timers and the time isn't long enough. So No.
One of the better ways is to make a phone call and talk to the rep explaining what you have to do and what they would recommend to be the least cost option. A DIP switch usually costs more, but the "resistor" if needed, you have to source somewhere else. The 24 VAC, the dry contact (NO or NC) requirement and the approximate 60 min timing, low cost etc. The DIP switch makes it easy to change the interval, so I would get prices and delivery for both.
I'll guess that your looking at $25 to $80 each. Yep, still messy.
The 60 min time isn't unusual. One would expect the "responsible adult" to hit it once or hit it for the expected time that one is going to be working "after hours". It does indicate that it's been hit.
A fix for 5 is not the same as a fix for 500.
The Carrier stat (unusual company), offers 15 min intervals, but I forget the maximum time ad hold indefinitely.
I am going at some point use a Vision Pro stat to create ersatz zoning in a laundry room. No duct there now. I have MOST of the parts. But occasionally, I'd like the clothes to dry faster or it to be cooler when the AC is on. The caveat is that the state of the register damper has to be either OPEN or CLOSED between say for 20 minutes or so around 1:00 Pm when the system does it's filter static pressure check.
The stat needs to have easy way to select 12 hours to a day max, and sometimes less.
Glad you like it here. I was very active in another forum on multiple boards (multiple topics) until an incident. I chose to leave because I was told that the mark would never be erased, but I was never "banned". I had some moderator privs there. I'm highly rated here and was there too.