Excuses for my ignorance, but how could I conclusively determine that?
More data. The patterns should become clear and either fit the analysis or not. Check different verbs and different word orders.
Can you give me an example or two?
You can look into Italian participle agreement with object clitics. I don't have a paper in mind and can't think of an example off the top of my head, but it's an interesting case where there's a small remnant of an older system still in the modern language. This also means it might be harder to be certain about what's going on in this language, if it's potentially grammaticalizing/changing.
If I can determine that there is no required agreement, then I can more comfortable claim that it is a real CC and not discontinuous, correct?
"real CC" and "not discontinuous" are the same thing, right? The word order may be due to something else.
That's an interesting question. Probably, I guess.
Can you elicit an example with a dative or other case? That would be interesting. Hard to say now whether it would be conclusive, but it would be helpful. I imagine something like this:
help-NMLZR-ACC want-3SG man-DAT
'He wants to help [to] the man.'
[I'm assuming dative case for 'help' as in German, just as an example. You can choose whatever verb you want.]