Agreed, and I would say I did acknowledge that some critiques of sentimentality are legitimate when I wrote "To be fair, I'm sure there are numerous instances where a film dips into schmaltziness due to how thick the sentimentalism is layered on, in addition to instances where sentimentality doesn't suit the tone of a film or scene." With that, I was explaining that I was referring to categorical objectors of sentimentality, not case-by-case objectors.
I think sentimentalism (as an evaluative pejorative) can be marked, on a case-by-case basis, by the following features.
1. Emotional Pentatonics. In music the easiest "go to" for writing and improvisation (vocally or in a guitar solo) is to play in the pentatonic scale. It is familiar, happy, predictable, requires no special skill and is a way to bribe the audience (like extra butter in cooked into a fancy restaurant dish). I speak of the emotions of the melodrama (e.g., joy, sadness, and outrage). Basically, the emotions associated with catharsis. Bad guy is bad and makes us sad. Our outrage demands that the man twirling his mustache must pay. Our damsel in distress is saved and we feel joy. Having this single feature is not, of course, sufficient to warrant the charge of sentimentalism. There are, after all, many excellent songs written (literally) in the pentatonic scale and many great artworks that touch on these cathartic emotions. That stated, when people complain of "sentimentalism," this is the color palate to which they're referring.
2. Compensation. The sentimental (in a bad sense) artwork typically makes this Pentatonic move as a compensation for some lacking feature. The subject-matter, for example, may be more appropriate for a more complicated emotional result (e.g., the sublime, ennui, melancholy), but the artist can't stick the landing so a "safer" and "easier" result is selected. In terms of emplotment, it's like getting out a tight corner, by announcing that most of what we saw "was just a dream" (e.g., a main character isn't dead, the MacGuffin is still MacGuffing) as an answer to the question "How will the Duke boys get our of this one?" as frozen frame featuring the General Lee flying midair as the network cuts to a commercial.
3. Incongruity. The objection, in the plainest of terms, arises when the emotional moment feels unearned, force, or false. Perhaps, the unhappy couple, both of whom have been cheating on the other, resolves their differences by putting an ad in the paper asking for a lover who likes Pina Colodas, and they "tomayto-tomahto" their prior mutual betrayals away in a romantic walk in the rain after one surprises the other by answering it. "Uh, didn't he still sleep with her mom? Didn't she burn down his hunting cabin?". This is why a heel-turn so often demands a death. Darth nuked Alderan, so he can't just rave with the Ewoks and hug it out with Leia and the end and call it good at the end of RotJ. The death-bed conversion frees our characters from the awkward emotional "walk of shame" the next day when you suddenly remember who you just embraced as a "goodie" or a "good enough".
I think Nolan tipped his hand as an artist when one of our characters in Inception created a psycho-hallucination-hustle arguing "What people crave most is catharsis." And my goodness, does Interstellar lay it on thick.