Learn English – Difference between “insensitive” and “not sensitive”

I think your understanding is definitely on the right track. In my view, "eloquent" is stronger and even more favorable connotatively than "articulate." Eloquent almost implies a talent at "elocution," the practice of oration or formal discourse, i.e., speaking well or convincingly in the manner of e.g. Cicero. Articulate implies the ability to elucidate one's thoughts clearly and succinctly but doesn't imply as much of a natural talent at speaking or persuading as "eloquent."

Ignoring the grammarian 'it is wrong' response, the 'standard' (for want of a better term) answer is that it is a quasi-passive. Fowler, for example, explains it as such in his Pocket Modern English Usage. The basic idea is that sentences such as "someone broke the car" and "the car needs fixing" are passive-like in function though not form as the actor is external and/or unknown.

Maybe more relevantly, the same idea allows the passive voice to have a continuum of function for the past participle from adjective-like to verb-like. In this, sentences like "I'm sat/I'm stood" are more adjective-like in function while "I'm sitting/I'm standing" are obviously more verb-like.

In short, "I'm sat here" is similar to "I'm big" or "I'm tall" - you are describing yourself more than saying what activity you are engaged in. In contrast "I'm sitting here" is saying what you are doing.

In the spirit of being fair, I am not 100% convinced by this explanation but neither can I think of a better one.