I was going to reply to your last post on original thread but figured I'd first check to see if you had taken my advice and posted here.
With grub4dos not working on the computer you want to install EasyOS to, How are you communicating with us? Or more to the point, are you booting into a OS on a USB-Key, from another computer or something else.
Hopefully, it's not "something else".
Perhaps someone more familiar with EasyOS has a better idea. But with my limited knowledge of EasyOS I'd suggest the below work-around to (a) overcome the road-block of Windows 10 requiring a UEFI boot-loader and (b) EasyOS not following the usual Puppy structure. Puppys are published as an ISO; EasyOS as an IMG. In creating a grub.cfg, Grub2config recognizes Puppys because all have core file systems begining with the word 'puppy'; e.g. fossapup64's core file system is named puppy_fossapup64_9.5.sfs. Even if these impediments could be overcome*, a deployed EasyOS occupies two partitions, while a Puppy only requires a folder for system files plus a boot-loader somewhere.
I don't think Windows 10 has (or can obtain) the tools you'll need. It's one thing to install EasyOS to a USB-Key; quite another to install it to the same hard-drive from which Windows 10 boots.
The work-around: create a functional Puppy Linux as an intermediate step. For example, install Fossapup64 to either a USB-Key or the hard-drive of the computer you want to run EasyOS on.
From a running Fossapup64, you can install the grub2config boot-loader which will OOTB boot both Windows 10 and Fossapup64. You can probably manually install EasyOS's files to however many partitions it needs after decompressing the EasyOS.img. You can also edit grub2config's grub.cfg file to provide a listing for EasyOS. [If you already have a boot-able EasyOS on a USB-Key, you have an example on that Key of the arguments EasyOS needs to boot. grub2config's listing for Fossapup64 provides an example of the arguments grub2 responds to].
Later, if all goes well and you want to, you can delete the Fossapup64's folder and its listing on grub.cfg. [But I'd leave it just in case something goes wrong in the future].
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* An Img can be decompressed and repackaged as an ISO, if necessary. But it probably isn't necessary as what I'm proposing is a 'manual install' of the contents of EasyOS.img.
IIRC, I was able to get grub2config to work with puli. Puli's core sfs also doesn't begin with the name 'puppy'. So I temporarily renamed it. Then once there was a listing for it on grub.cfg, I changed the name back to just puli.sfs and edited the grub.cfg listing.