I invested in a puppy pen. eight 2' wide panels of coated wire. I put reinforced hardware cloth across the top (with zip ties) and set the heat lamps on that. Used 6 mil plastic underneath and up the sides, with towels for bedding (my allergies - otherwise would have switched sooner to shavings).
The puppy pen served as an emergency shelter in the basement until I built a more permanent indoor pen.
If you or a friend are handy, building a rectangular box frame and then using hardware cloth on the bottom (covered with a towel or no-skid soft mesh) and plastic poultry fence or hardware cloth for the sides could work. That's what I plan to build for my next batch of babies. I like the idea of putting it up on legs as well, for ease of access and avoiding the "looming human" issue when they hit three weeks of age.
Do you have pics of your babies?