The Collage Coding Method for solving inverse problems has been well established theoretically. However, in practice, a number of computational considerations arise during implementation that depend on the complexity of the problem at hand. In this paper, we review the theoretical underpinnings of the Collage Coding Method for solving inverse problems for first-order initial value problems. We then present a comprehensive investigation of computational challenges and choices that may be faced during numerical implementation. Examples showcasing the results of this investigation are presented and discussed.