Couple tips:
first, as suggested make certain the leak is not from the quick connect couplers on the firewall. Usually these just leak externally down the firewall. Even if they are OK, I'd get new ones since they'll have to come off anyway to do the core and they are a common source of leaks (little o-ring inside).
second, you really do need to look into the HVAC door foam. This is very common, more common than heater core failures actually. You can either buy a new case (comes complete with a new evaporator core and expansion valve, but oddly not the heater core itself
) or if you want to take the time you can take it apart and refoam the doors. Either way, this is not a job you'll want to do again in a year or two because the foam starts to fall off the doors.
You may also want to get some new foam gaskets for the blower case to the bottom side of the body/firewall, as well as the cabin filter tray holder to body, and possibly the center duct(s) (you will see what I am talking about when you get in there).
This is NOT a bad job. It really isn't. It is just a bit tedious and time consuming. If you have never done one, or never done anything like this (lots of cars require dash R&R for all kinds of things), then you may not want to give yourself any "deadline" for the task. Leave it open ended, arrange to have another car to drive if need be. This is not something you can rush.
This is also a good opportunity to clean a bunch of hard to get to interior bits, and replace anything that is broken (glove box, center console, cupholder, etc.).
And I *think* the shop manual leaves out the hidden brace bolt under the wiper motor, can't remember (been so long since I had need to look this procedure up, but I seem to recall something like that my first time). So if it doesn't say so, the wiper arms, cowl trim, and wiper motor, need to come out to get at this bolt.
Also, the brace does NOT need to come completely out, just needs to come loose enough to weasel the HVAC case down and out from under it. However, if you want to take the time, removal of the brace completely is not hard. You just have a lot of wire harness holders and things that need to come off.
It is helpful to take pictures as you go, so you know the proper routing of wires, etc. Also, the defrost duct is sandwiched between the brace and body. Pop it loose (straight up) with the brace in place, then once the brace is loose, take it out. Then do not forget to set it loosely back in place BEFORE you put the brace back in place. Then once the brace is in place, pop it back in to its holder. You will see what I mean when you are in there.
Good luck! Ask if you have any questions. I do a lot of these.