KJV For where two or three are gathered together in my
name, there am I in the midst of them.
NRS For where two or three are gathered in my
name, I am there among them."
In the biblical expression used here, whether it contains an inversion (KJV - Early Modern English) or not (NRS - Modern English), there is used as an adverb and not as a dummy subject, as it is the case in your example, There is me in this house (which, I agree, is unusual and may be possible in very particular contexts as indicated in the comments).
I don't speak Hebrew, but the Greek version of this expression [ἐκεῖ εἰμι - there am] confirms that there means in that place and functions as an adjunct of place. It is emphatic, the sentence could stand without it:
I am among them (NRS)
But in the KJV version, the omission of there will no longer require an inversion:
I am in the midst of them (KJV)
As for the use of there is/are with a personal pronoun, it is indeed rare, but not completely non-existent. A wild-card chart in GNgram shows you
- that the use of there is me has recently seen a mild increase.
- that often another word (preposition or adverb) will come between there is and the personal pronoun.
You can find it in literature, as a way of introducing a character:
There is me, and own God-Master. There is Slippers, and Slippers's Own God-Missus. That is all my paws. There is Adar. There is Cookey. (The Complete Works of Rudyard Kipling)
And you could probably use this expression while describing a photo or a video. This following excerpt seems to be describing a scene in a vivid way:
But no, instead there is a mere bishop, there is the king, there is me in a bewitching gown of gray-green silk that shifts colors as I move... (The Boleyn Inheritance by Philippa Gregory, Page 317).