Honestly, I didn't try. But if an infected person could produce 1-100 billion virus particles, and each virus particle has 20-40 spike proteins, that means 20-4000 billion spike proteins.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7665311/

For mRNA vaccine, I'm not sure about the calculations though. Yuri Deigin calculated 12 trillion mRNA in a 30mcg Pfizer's vaccine. If each mRNA can give rise to 10-100 proteins before being degraded, that would mean 120-1200 trillion (120000-1200000 billion) spike proteins. But I'm not sure if Yuri's calculations are accurate, if all the 12 trillion mRNA gets translated in the body, and if each mRNA really produces 10-100 spike proteins.

https://yurideigin.medium.com/get-vaccinated-it-could-help-you-like-not-die-71ebf63555f4

But if the actual scenario is somewhere close to these numbers, then I believe you are right that the mRNA vaccine makes the body produces more spike proteins than a typical SARS-CoV-2 infection. Still, at least the mRNA vaccine-related spike proteins are in the prefusion ('closed') state, not the post-fusion one.