The effect of gene expression burden on engineered cells has motivated the use of “whole-cell models” (WCMs) that use shared cellular resources to predict how unnatural gene expression affects cell growth. A common problem with many WCMs is their inability to capture translation in sufficient detail to consider the impact of ribosomal queue formation on mRNA transcripts. To address this, we have built a “stochastic cell calculator” (StoCellAtor) that combines a modified TASEP with a stochastic implementation of an existing WCM. We show how our framework can be used to link a synthetic construct’s modular design (promoter, ribosome binding site (RBS) and codon composition) to protein yield during continuous culture, with a particular focus on the effects of low-efficiency codons and their impact on ribosomal queues. Through our analysis, we recover design principles previously established in our work on burden-sensing strategies, namely that changing promoter strength is often a more efficient way to increase protein yield than RBS strength. Importantly, however, we show how these design implications can change depending on both the duration of protein expression, and on the presence of ribosomal queues.