Further research has resulted in mixed information and no clear solution.
Our solution is to use a separate file and execute the script using CRON via the command-line, rather than relying on the WordPress cron system. This has the added bonus of max_execution_time=0 as well. PHP Max execution time
Stripe’s API seems to take about 2-3 seconds to process a transaction. If we limit our WP_User_Query to 100 users, that should take roughly 300-500 seconds to process an entire batch.
Since we are planning to execute our script hourly, I used set_time_limit=3500 (slightly under an hour), that way if something goes wrong it will be terminated before CRON executes the script again.