Recently discovered CRISPR-associated transposons (CASTs) are natural RNA-guided DNA transposition systems capable of single-step genomic integration of large DNA cargo. Wild-type CASTs exhibit low integration activity in heterologous systems; therefore, engineering efforts are required to develop therapeutically relevant tools. Here we developed a high-throughput dual genetic screen capable of accurately quantifying the relative activity and specificity of a large pool of CAST variants. Under the conditions of our screen, we discovered that the wild-type V-K CAST system can consistently achieve between 88% and 95% on-site targeting specificity. We used site-saturation mutagenesis of the conserved core transposition machinery (TnsB, TnsC, and TniQ) to reveal novel mechanistic insights into the function of these transposon proteins. Furthermore, we found that different components have varying trade-offs between activity and specificity, a critical aspect overlooked in conventional screening pipelines. These findings provide clear engineering principles for further optimization of CASTs. Finally, we identified several mutations that, together, enhance CAST activity up to four-fold while minimally impacting targeting specificity. These methods are a powerful tool to characterize the sequence-function landscape across multiple functional parameters while also providing a robust platform for developing enhanced genome-editing tools.