Good morning, forgive my ignorance first of all.. the other day I acquired a new SD with a higher capacity, I thought that it would not be something so difficult for me but this is how it is, first I use iMac, I do not have physical access to Windows, I have tried to clone my SD on Mac with different programs (Paragon, HDM and Carbon Copy) none have worked, I think the problem is that my partition is hidden.. I have an SX chip with Hekate and AMS .. in a virtual windows of Windows 7 either I have been able to do nothing, neither with Emutool nor Minidisk Wizard Tool.. I am desperate and I don't know what I can try..
I went from a 128GB card to a 1TB one today and used this guide https://nh-server.github.io/switch-guide/extras/transfer_sd/ following the "If you are using a partition based emummc" section as I had already made a partition based emummc.
I'm on atmosphere though on a launch Switch, so no SX chip, and I'm using Windows. But hopefully that guide can help you. Your issue may be that you assume you need to clone your old SD card to your new one, as if you were changing a boot drive on Windows or whatever, but that isn't actually the case.