You could set Windows machines up to accept RDP connections. This is a windows specific remote access and might need a bit of configuring. Essentially it works the same as teamviewer.
Concerning your warning message from Teamviewer: I am not totally sure how they classify commercial use. Probably they mean using Teamviewer for remote maintenance etc. in a business context. As you are operating on your own machines for your own benefit, you are likely still using it as what Teamviewer considers personal use.

What features do you need? You probably just want to monitor and restart miners. RDP is absolutely sufficient for that.