Issues with booting Zorin OS on HP tablet

This may be a mixed bit-depth issue: your tablet may have a 32bit EFI even if the CPU is 64bit and Zorin (because of its Ubuntu base) does not support 32bit any more. Unfortunately, the process of making bootable linux USB drives often includes a 32bit bootloader, which then hands over to the 64bit Zorin live environment and lets you install it.

After trying to follow a bunch of tutorials and forum threads I couldn't get to work, I ended up installing a different linux distro that does still support 32bit, specifically Linux Mint Debian Edition (LMDE), first to get its 32bit grub installed and then manually install Zorin next to it while carefully selecting the EFI partition - the last bit is important, as it means Zorin just adds its own config instead of actually trying to install / replace grub with a 64bit version.

That said, I had notably more space than your tablet. I'm not sure if this method works if you install Zorin over LMDE instead of next to it, but I'd say it's worth a try.

At one point, I also ran into the tablet claiming there was no bootable drive at all. To fix that, I actually tried reinstalling Windows and after confirming that booted I then went back to install LMDE and finally Zorin, successfully.