[Milhouse]

How do I select the HTPC drive over the network?

I doubt you can (unless using something like iscsi) as you need to directly connect the drive to the host in order to access the partitions tables, which isn't usually accessible when mounting disks over a network.

As per the note in the first post you can try booting the HTPC with a LiveCD/LiveUSB (eg. SystemRescueCD) and then use gparted to resize the partitions - it only takes a few minutes.

Alternatively, backup your existing data using the LibreELEC Settings "backup" option, install LibreELEC from an official disk image (this will create a 512MB FAT partition while also wiping all your data), then restore your data. You should then be able to upgrade to one of these test builds.

Edit: Or remove the drive from the HTPC and connect it to your PC that is running Mini Partition Tool. Personally, I'd take the LiveCD/LiveUSB approach.