The ‘gerund’ for the English language is a problematic idea. I have already written about it in other answers on this site. And my view of gerunds is one with which many would disagree.
First, the term ‘gerund’ is derived from a Latin form: English ‘gerunds’ end in ‘-ing’ while Latin ones end in ‘-ndum’. The gerund has no plural form - or, at least, there is no evidence of its use in the plural.
That suggests its use was modal. It presents an action or event not as something specific in time and space but as a type of action or event.
S/he reached the island by swimming = Ad insulam nando pervenit. This expresses how s/he got there.
I’ve been to London to look at the queen = Londinium ivi ad reginam spectandum (or ... reginam spectandi causa). Again, we are writing not about the specific action of looking but the purpose of the pussy cat’s going - why s/he went.
A Latin gerund can never stand as either subject or object of a verb. Its role, in truth, is adverbial. It modifies another verb ... in Latin, that is.
So the main common factor between Latin -ndum and English -ing words is that they are verbal nouns.
But that being said, there are important differences. First is that -ing words can also be participles, which are adjectives, as with ‘being’ in my previous sentence.
Second, in English, so-called ‘gerunds’ can be subjects or objects of verbs.
I resent your inviting our friends to dinner when you knew I am working late.
Running away won’t save you.
So what about a plural? There are gerund-looking ‘-ing’ words with , like the word ‘feeling(s)’, which you cited, that have a plural. ‘Beginning’ is another; ‘killing’ is another still.
My personal view is that our use of the word ‘gerund’ is already stretching the Latin form. Its use in sentences in the role of subject or object stretches it further.
Once we see a plural form, like ‘feeling(s)’, a further stretch has occurred. We can use them with the indefinite and indefinite articles, and we can count them. Indeed, all of a sudden we cannot modify them with adverbs: we can only qualify them with adjectives.
”Do not be surprised by my suddenly feeling your pocket: I saw you take my credit card”..
Of course, you could say “Do not mind my sudden feeling of your pocket etc...”, but it would sound clumsy. But
I was seized by a sudden feeling of panic
or: I was aware of two contradictory feelings: one of relief and one of resentment.
It is possible just to go on calling this verbal noun with a plural a gerund. usage is like that: it can change. But another way of looking at it, is that the verbal noun has evolved into a fully fledged noun, derived from the verb ‘to feel’. Like ‘beginning’, ‘meeting’, ‘seating’ and many others, it is behaving no differently from any other noun.
But to return to your original question!. I would argue that your “people dancing together” is a grammatical contradiction that works out in the end. It works in the end because as long as we don’t think about it too hard, we understand it.
My generation of English speakers for years corrected the increasingly common tendency to say things like: “I resent you talking to me like that.”. No, it’s “your talking: its a gerund!. Eventually, we, like Canute, gave up. We still have to accept that dancing is a participle qualifying people in “I see people dancing in the street”. We might be OK with “People dancing in the street are a nuisance”. But “People dancing in the street are against the law” is a bridge too far. It is the word dancing that is the object of the verb. People’s dancing sounds silly. So my generation avoided it and found another way round. Now that we have given up, all we can say is that ‘dancing’ is serving both as a participle (qualifying people) and a ‘gerund’ (subject of the verb and singular). Like quantum physics, it shouldn’t work, but it does. That is the beauty of English.