I would keep checking online every day to see if a reservation for 3 comes up. Since TH is a character meal restaurant people will cancel when their plans change to avoid the $10 per person no show/no cancel fee.
If you can't find a res for 3, try adding a person and look for a res for 4. The Disney res system has a quirk that makes it harder for odd numbered parties to find a res because the system wants to fill every seat at a table. Thus, a party of 3 which would usually be seated at a 4 top is passed over. Try for a party of 4 and something might open up. When you get to the restaurant just tell the CMs at the podium that you are a party of 3. As long as at least one person shows up for the res, you won't be charged the no show fee for the "missing" person.
Also, it's much easier to show up with fewer people than try to add extra people at the restaurant. While it's unlikely one person in your group will be turned away if you show up with a res for 2, it's always a possibility because of fire and safety code rules regarding room capacity.