No matter what you use to do the disk check, it's always actually done by the Dos and no matter what, no user program has enough priviledges over the Dos for security reasons. Windows and generally only the OS is allowed to interract with it, reason why we get things like CMD or PowerShell. Disk check done during startup is done after the BIOS loads and before Windows does, so no program can interfere with it more than just call for the commands to be executed. The algorithm is exactly the same for those commands. Letting everyone just mess with the command instructions and algorithms would only increase security risks and could cause parts to fail. Better use a code that's guaranteed to work rather than one that may fry parts by accident, right?
You CAN change the algorithm for disk checks and Dos commands though if you modify the Dos itself or are on OSs with increased functionality such as Ubuntu/Windows 2016/etc. (generally supercomputer/server OSs).
On topic now, thinking about this, I get a feeling the issue is somewhere no one mentioned... It's VERY likely it's the PSU causing the issue, it may suddenly give less charge, not enough to shut down, but enough to cause everything to hang and once something hangs due to low power, even if it goes back to normal it will stay frozen. Did you try pulling out any network cables by the way when it froze last time like I suggested? When it freezes, just pull out the network cable or whatever you are using and if it unfreezes it means that the issue is there. Additionally, do the fans just go crazy and get all loud when it freezes? I got a hunch...