Hi,
The Push Button Reset partition was created by Gateway.. It is a feature of the machine...
You may have a hot key to hit at the Gateway screen when you boot, and maybe not..
There may also be a method to launch it from within Bios..
It may also be accessible from within Windows by some type of application.. If it works, and I have serious doubts about that, it would do no more than return your machine to it's original Factory setup..
That is why one of the .WIM files is "Bloated" as PCR describes it.. It is not just Windows 8, but probably also full of Gateways other pre-installed stuff.. I wouldn't know why you would ever want to factory reset to Windows 8 anyway, even if it were possible..
As I mentioned before.. You could most likely delete the 800mb Recovery and Push Button Reset on your current HDD and then recover them from one of your other images to your current HDD..
It is possible that the partitions are not as they should be anyway, as a resut of all the manipulation using Partition Wizard.. Some of the stuff you mentioned concerning "Merging" could have done some "Copying of files" in the process.. It seems to have resulted in the desired end result as far as everything else, but could have made a mess of those two.. "Merging" means to "Combine".. What you really wanted to do was to "Move" or "Relocate" the partitions... But I haven't checked the available options in partition Wizard for quite some time..
I think you are wasting your time forcing Acronis to image two bad partitions.. If they are corrupt, they are most likely useless, but maybe not..