Using LVM makes it really easy to resize the disks on the fly. But most important is to place the partition that is going to be resized at the end of the disk during installation.
For example, traditionally swap partitions are placed are the end of the disk. For VMs it's better to place them at the start and the root partition at the end, so you only need to ...
I plugged all the HDDs into a second SATA controller, which resolved the issue. No more freezes for a whole month. Apparently my theory was true; I assumed some timout during the high load HDD activity would cause the whole controller to freeze, thus blocking access to swap. When swap was disabled, there were also no freezes.
Clear-Disk does not uninitialize removable media, only disks (HDD, SSD, VHD, etc.). To change the partition style of a removable medium, you can use Set-Disk with the -PartitionStyle parameter:
Set-Disk -Number 5 -PartitionStyle MBR
To view an example on how you can use Set-Disk inside a pipeline, you can have a look at my question on SO.