Is this padded version of the Halting Problem in NP?
Unless you're talking about promise problems, you are required to handle arbitrary inputs. 

Given a string $x\in\left\{0,1\right\}^*$, we have $x\in L$ iff $x=\langle M\rangle \cdot BB\left(|M|\right)$ and $M$ halts for some fixed input ($\cdot$ denotes concatenation).

This means that even before talking about the witness (which is indeed linear), you must verify that $x$ has this specific form (unlike in promise problems, where you only care about specific inputs), and this is undecidable.

Note that this only shows why your justification to why this problem is in NP does not work. However, this language is obviously undecidable, since otherwise you could compute $BB(x)$, and thus lies outside of NP.