To start, it's not legal. If the people you are hiring are doing the same work as full time employees, with the same work structure, you're not supposed to hire them as contractors.
> Or spin up a separate company and buy services from them?
I mean, companies certainly do outsource to third parties for "bursty" needs, but if you think this is going to be an important core part of your business going forward, why would you go through the organizational complexity to spin up a new entity? How would you explain this to recruits? "Congrats, you've been hired by the slightly shittier version of us, and when layoffs come you'll be the first to get cut." I mean, companies do actually kinda do that, but it's very much a hierarchical system - anyone with the ability to get hired by "main company" is not going to take a position with "shitty clone".