Hey there, @j2manderson.
Thanks for posting your question here.
If you want to print a copy of an e-filed 1099, you can access your 1099 E-File Service account. Then, download the form and print it from there.
You can open this article and proceed to the Can I access archived/previously filed forms section: 1099 E-File Service FAQs.
Please let me know if the steps above do the trick. If you have any more questions or concerns, please don't hesitate to reach back out.