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You might want to take a look at Genie Timeline.
Genie-soft Free Timeline | Download Free Backup Software for Windows
I use Macrium Reflect, which does have a free version, it does an image backup real-time, and it is fairly fast (at least, compared to Acronis), and there is an option to set priority -- but I don't know about minimizing RAM usage.
You're asking for a LOT from free software!
Here is a Macrium tutorial: Imaging with free Macrium And here is the time it takes to backup my C partition: