I have to admit, I am not sure exactly how I would approach this myself, least of all when dogs are involved (my own two dogs are the very reason I will soon have to do the exact thing you're facing right now). I am assuming you are most concerned about the time to cure for full strength (1-3 weeks), not the time until it's no longer tacky (3 hours), right? My guess is that you can speed up evaporation of the thinners (the first 3 hours) by placing a strong fan at the bottom end of the stairs and aiming it up. Use a large box fan - it will move more air and hopefully block access for the dogs (or the noise will keep them away). Not much can be done to speed up the actual curing time though - it's a chemical reaction, dependent on temperature and oxygen. Other than doing it during the hottest and driest season, the reaction should just run its course.
If there will be a runner in the middle, you might want to make sure you walk only over the center path, just wide enough to be eventually covered with the runner, even if it's covered with rosin paper while curing. It's not supposed to be subjected even to light use within the first 24 hours or so. So, if you absolutely have to walk on it, do it over the part that will get covered later.
Another suggestion I may have is to ship everyone with the dogs on a nice 72 hour extended weekend stay at a cabin someplace and join them yourself after you applied the second coat (in 6 hours after the first or just about). When you return, it will already be possible to throw the actual runner on the stairs and walk on it (and hope the dogs behave - that might just be the hardest part).
Good luck! I hope it goes well, and if you can come back and tell us about your experiences, it will be awesome!
- posted 7 years ago