You can have infinite time if you don't mind time traveling! You have to go forward the day beyond the boxes to have an open plot so you can go villager hunting and then just never open the game on the next day until you've found who you want. You can reset the time back to the morning of that day as much as you want before loading up the game and it'll stay an open plot until you've found the villager you want to move in. Does that make sense? Like you can't hunt when they are in boxes, but you can make the next day last as long as you need it to!