OP,
I haven’t read the entire thread, but several thoughts come to mind regarding your understandable concerns.
You keep referring to “private” catholic schools. I do not think it appropriate to call your typical parish school “private”, as they are intended to provide catholic education for all parishioners children . Now, there are catholic schools, often run by religious orders, which do seem more private in nature: ie they are more selective with students and tupically cost much more. If you are referring to the latter, you local parish school migt solve your problems. Our, for example, provides reduced rates for each child, down to zero for the 4th. Also financial Sid programs are often in place, many pastors take the attitude that no one should be turned away because of money.
Finally, your kids are young. It’s good to plan ahead, but trust God. Jesus taught us to pray " give us this day…", not “give us this year/decade…” I have always thought it best to take the attitude, if I can afford another kid now, I will figure it out by the time the real expenses kick in. Having several kids to provide for and educate is a heck if a motivation for a husband.