My name isXXXXX a licensed attorney. Glad to try and help out.
Sure sorry for the circumstances, truly. My heart goes out to you.
Here's how this works. As you astutely mentioned, the law codifies a rebutable presumption, as follows:
Missouri Revised Statutes § 210.822
However, in today's age of paternity testing, so much of this has fallen into little relevancy. In other words, this was all much more important back in the days when Courts ended up calculating gestational periods and so forth.
As to how "easy" a given case would be, in all candor there's just no way to say until the litigation is underway. It would be meaningless and unethical for me to recklessly say "very easy" or "very difficult" or anything along similar lines. It's somewhat like asking a surgeon is removal of a tumor would be "easy". Well, some are quite easy and some are incredibly complex. Until the surgeon is in the middle of the procedure, or at least has a chance to review all the scans and so forth, he or she just can't say. Likewise, here, without going to Court, conducting Discovery, reviewing the case files and so on, there's no way to say, beyond pointing to the statute.
Having said all of that, though, what I can say with absolute certainty is that science is king these days. Meaning, these cases hinge on the scientific evidence, and if you meet that statutory standard, you win the case.
I would love to say otherwise, but I just feel compelled to be honest rather than misleading you.
If you have a follow-up question or need clarification, please just say the word by using "reply" to reach me.
I truly hope all works out for you.