Have you seen Packer-Raeburn Stabilization trick? 

>Judith A. Packer and Iain Raeburn, _On the structure of twisted group $C^*$-algebras_, Trans. Amer. Math. Soc. **334** no 2 (1992), 685-718, doi:[10.1090/S0002-9947-1992-1078249-7](https://doi.org/10.1090/S0002-9947-1992-1078249-7)

Specially Theorem 3.4 therein establishes that the algebra is Morita equivalent to a Twisted Group $C^*$-algebra, summarizing the answer by N. Ozawa and the correction above. 

By considering the trick of viewing the algebra $K\rtimes G$ as a locally trivial bundle with a $G$-action over a contractible $G$-space $X$ (for instance, the total space of the universal $G$-Bundle $EG$, but also the space $\underline{E}G$ works), you can see the $C^*$-algebra in question is Morita equivalent to the algebra of sections of the Fell bundle over the transformation groupoid $X\rtimes G$. This has been documented in Kumjian's monograph 

>Alex Kumjian, _On equivariant sheaf cohomology and elementary $C^*$-bundles_, J. Operator Theory **20** (1988), no. 2, 207–240 ([journal pdf](http://www.theta.ro/jot/archive/1988-020-002/1988-020-002-002.pdf))

Other references on this kind of tricks include 

>Siegfried Echterhoff, _Morita Equivalent Twisted Actions and a New Version of the Packer-Raeburn Stabilization Trick_, Journal of the London Mathematical Society **50** Issue 1 (1994) 170–186, doi:[10.1112/jlms/50.1.170](https://doi.org/10.1112/jlms/50.1.170)

and part 5 here: 

>Noé Bárcenas, _Twisted geometric K-homology for proper actions of discrete groups_, Journal of Topology and Analysis (2018) doi:[10.1142/S1793525319500729](https://doi.org/10.1142/S1793525319500729), arXiv:[1501.06050](https://arxiv.org/abs/1501.06050).