Combining Overhead Press and Bench Press

Hi CT, been lurking on this site for 7+ years, and have followed your work along the way.
Is it possible to start a bench press workout with standing pin press or strict press, then move onto the bench press workout? My main goal is to increase my bench press and I find that I feel more “awake” when I bench as a second movement. I’m thinking something like this
Strict press ramp 3,2,1
2 cluster sets 90%
Bench press ramp 1rm
2 clusters 90%
Bench press ramp 2rm
2 clusters 90%
85% 2rm max reps 15sec max reps
4-6x3 50-70%

Thanks in advance