Software often gets more demanding as you upgrade, because there's often newer hardware that can run faster.
I don't know though. Another google tells me that my GPU is 520% better than yours
And your GPU is also a generation behind the minimum requirement of Intel HD 4000
I'm not sure how to deal with that other than buying a new computer, but maybe trying the following will help.
1. Downgrade minecraft. Maybe your 60FPS result was from 1.12, or 1.7.10. Downgrading Minecraft could get you better results.
2. Turn down your chunk render distance, stick to fast graphics? though you probably already did it.
3. Mod your minecraft with performance improving mods, I prefer Sodium/Lithium/Phosphor, but maybe you can use something else?
4. If you believe Windows 10 is hogging all your resources, then you might want to use Linux. Though I'm not sure if your computer can handle fully graphical linux (I don't think you would like command prompt only) and Minecraft at the same time.
In my opinion, this isn't a problem of Mineshafter, as Mineshafter is the launcher that allows you to play the full version.
You can try to play the demo (as Mojang suggests) to see if you get better performance