You say domains
To ensure we're speaking to, not past, each other it will be essential to clarify one thing: what do you mean precisely by "setting up new domains", "cheap/ free domains"?
Domains, I'm not interested in chatting about those, but IP address space, then yes I'm all ears. If you can reliably setup new, fully self-hosted mail servers (i.e., not using SendGrid, MailGun etc), with port 25 open for both send and receive, on cheap, accessible VPS servers...
And...
Send email messages from those new servers directly to your Outlook's inbox.
Then you Good Sir, have the secret sauce.
*Caveat: AWS does have a lot of un-blacklisted IP address space, however, port 25 remains blocked for new customers without a "valid use-case" and an unspecified amount of payment history. Similar for Azure. So if your methodology is built around AWS/Azure then kudos, but for new-comers, it would be unrealistic from my experience to suggest the path forward will be without major hurdles and/or delays.
The lack of verbose feedback in the rejection reason from Outlook was, as I see it, a feature not a bug. A bit of friction to turn away the undetermined ones. I followed the trail of clues from the top search results of the error message and eventually got my new IP unblocked through the proper channel. So... I have made it from bottom tier (outright rejection of emails), to 2nd-bottom tier (directly to spam/junk folder). Next: build domain/ip reputation ever so slowly.