We can definitely get by running the sampling on a dozen larger systems, but those systems still cost more than (one thousand Lambda executions * a few hundred times a week max).
Pre-computing is an interesting idea, but would certainly be an epic amount of work. The input set is also quite large (compiled motorsports data based on current state of an event).
I'm also totally willing to admit I'm probably in over my head in designing such a system, but I did try a few different ways of architecting this and tweaking the parallelization in the source and this was the best cross of time/money I could get! It's definitely been a learning process for me; although I've got some years experience with scaling out, the system and requirements were much different than I've been exposed to. I'm sure this first take will be changed or at least refined once it's been in use for awhile.
This may come off as arrogant, but it sounds like something that could be rewritten in Fortran to run on an old laptop with similar execution time.