I have no direct information what the songwriter wanted to say, but here are some linguistical considerations, and an attempt to interpret the text of the last line.
Supposed the transcript is correct: the last line could actually be meant as
Wohlstand gehört nur in den Bauch.
Which can sound in sloppy pronunciation like
Wohlstand gehört nur in'n Bauch.
That's simply a very prolonged "n" between i and Bauch. That's a very common way of speaking in everyday situations.
Grammatically (but not orthographically) the sentence would be okay then.
You are right with your assumption that this way of blurring sounds around articles and prepositions, and reducing them to basically only an "n", occurs also in a popular form of pronouncing
In den Wald hineinspaziert
Innnnn Wald hineinspaziert
(I vary the spelling here; I could have spelled in'n likewise, or in''n for more precision - one apostrophe replacing one left out letter.)
And the meaning?
I can not definitely tell what the author wants to say by this. For me, the most probable interpretation seems to be something like:
We do not need luxury and comfort such as well-equiped homes, but we should have good food.
Whether that's what the author wanted to say - nobody knows but him. Songwriters are often a big vague in their texts.
More funny phrases
Hennenstall --> Hennnnnnstall (Henn'nstall)
It would actually even be wrong to speak the second e in Hennen.
In den Hennenstall --> Innnn Hennnnstall
Okay, that's sloppy pronuncation now. But definitely existing.
Kann ich mal ein Ei haben? --> Kannich maln Ei hamm?
Wenn Sie wollen, können Sie gehen. --> Wennse wolln, könnse gehn.
Im Leinenanzug bis zum Knöchel im Wasser --> Im Leinnnanzug bis zum Knöchl im Wassa