What about the 3M Fastbond 30NF contact cement? The technical data sheet from 3M even mentions hardboard so I would hope it would work. It is very expensive at three to four times what regular DAP flammable contact cement sells for. It is available through Amazon Prime.
The easy choice would be to just keep using the regular contact cement. It should work just fine. It just needs a lot of ventilation to use. The dew point and temperature have been unusually low for the past few days so bringing in lots of fresh air has not been an issue. The dew point will be back up into the 60s by tomorrow so bringing lots of humid air inside is not a great idea. I will probably move the operation outside to keep the chemicals outside.