Thanks for checking in! In short, I was able to produce similar results.
After looking more closely at the input matrices from the two pipelines, I realized there was an error with the column order which I was able to resolve. I then reran the analysis and got much more similar numbers of differential genes.
Attached is a quick graphic I made to compare the outcomes for 4 different comparisons I made from the two matrices. The results from the matrix I generated manually are labeled STAR. The core pipeline matrix results are labeled as Salmon. For comparisons 3 and 4, nearly all the DEGs I called were also called in the core pipeline. There's some disparity with comparisons 1 and 2, but the effect from those conditions is fairly small so I was not overly concerned with a lack of overlap there.
As for the large fold change values shown in the image I shared previously, if you apply a log2 to them you get roughly the log2 fold change reported by my own calculation.
Overall this data isn't rich with differential genes in either analysis. However, the results from the two analyses are generally similar.
Thank you guys for your support in trying to figure out what was going on!