i wouldn't really recommend doing this if you're using the foolproof method, as cycling with this method is pretty fast and you'll get every villager eventually if you cycle long enough.
if your boxes day is may 15th 2016, you'll TT back to may 10th, 2015. then your next step would be to TT to may 10, 2016. on that load of the game, a new villager will be plotted. if you want to try to reset for a specific villager, load up your game at 5:58am as you would for plot resetting, and then save & quit. load up the game again with a new save file and blah blah blah, you know the rest. keep in mind, loading up the game at 5:58 is the same as loading it up on the previous day, so there's a 99.9% chance doing so will mess up your cycle, meaning when you finally get the villager you want and TT to your boxes day, it's most likely no one will be in boxes, and you'll need to change your boxes day and start cycling all over again. another thing to keep in mind is that resetting for one specific villager is extremely tedious and usually relies on whichever personality your town is missing. for example, if marshal was your last move-out and you have no other smug villagers, the next villager to move in is almost always going to be smug, so you couldn't reset for any villager other than a smug.
i've never tried this personally, as i cycle for a long time and within a few months will usually go through every single villager, but if you'd like to give it a try, let me know how it goes. if you're looking for specific villagers, you may just want to reset for each random move-in when you first start the town rather than during cycling, or just not use this method of cycling at all. good luck! c: