ネタ Slang Word and Help Understanding Song Lyric

Question

I encountered the following lyric from the song, 夜咄ディセイブ, and I'm having some trouble understanding/translating it. It also doesn't help that the available translations of this line are wildly different.

ネタ話だって 体{てい}で 一つどう？

Here are the two available translations of the lyric online. I believe neither are official translations, so they might not be correct or are perhaps taking artistic liberties.

It's just a short tale; you up for one?

How about I provide you an interesting story for a reasonable price?

I get what the slang ネタ means generally from this question, but from my searches, as with most slang, the term is very flexible and can attach in weird ways that alter the meaning of a word.

Various sources I've found (indirectly) suggest it could mean joke story, tall tale, or the interesting part of a story (i.e. the seed of it). The first one I could potentially see working, but the second one seems strange since the term 法螺話 means exactly that, and that term is used later on in the song in a different context. The third one I could also maybe see working, which would give us the "interesting story" translation from above, but it's a bit unclear.

As for the rest of the sentence, there isn't really a verb, but I'm guessing there's an omitted ですか at the end since it's a song lyric, and it's pretty informal (also guessing there's an omitted は for ネタ話). 一つどう also is fine, it's basically asking if the listener is okay with trying something out.

However, I'm unsure what 体で is doing exactly in this sentence either. The definitions for this reading of the kanji give me "appearance; air; condition; state; form," but none of those really seem to fit here? Any insight would be very helpful.

I guess to put my points of confusion more succinctly for an answer:

1. Does the term ネタ話 have an established meaning or could it mean any of those things based on context?
2. What is the role of 体で in this sentence? Is it a weird interaction with どう or am I missing something really simple?

In case additional context is needed, here is the full verse that the line comes from, each line separated by XX because I'm unsure on formatting.

ねぇ ちょっと話そうか XX 馬鹿な自傷症性なんだけど XX もう なんか収まらない XX ネタ話だって 体で 一つどう？

Answer 1

ネタ is probably used in the sense of "non-truth".

https://kotobank.jp/word/%E3%81%AD%E3%81%9F-595058

５ 人をかつぐための、真実めかした作り話。悪意のある嘘ではなく、相手を笑わせたり軽くからかったりする程度である場合をいう。「彼の失敗談はねただろう」

てい (体) in this context means "pretense".

https://kotobank.jp/word/%E4%BD%93-90708

２ 見せかけ。体裁。「―のいい返事」

With the context of the speaker wanting to tell a tale in mind, ネタ話だって体で sounds like "let's pretend that this story [that I'm about to tell] is not about a real event". They are probably saying that they want to talk about "self harm" (judging by 自傷症性なんだけど), which actually happened, under the pretense of telling a fictitious tale.