OK, I started over. Re-partitioned both the SSD and the USB in Mac OS X as GPT disks with 1 FAT32 partition. Transferred USB stick to DH87RL, entered BIOS UEFI shell, verified no files exist.
Transferred USB to Linux Mint 15 32-bit system, and used UNetBootin to copy Linux Mint 16 Cinnamon 64-bit ISO to USB second partition. Transferred both USB and SSD to new system with DH87RL board, Core i3-4130. Set BIOS to UEFI only. SSD not recognised as bootable, only USB recognised as bootable.
Entered BIOS UEFI shell, verified NO files exist in fs0:\
USB stick boots perfectly, with GRUB selection screen. Ran Linux Mint 16 Installer, installed to SSD, manual partitioning: EFI system partition, root partition formatted as ext4, no swap, bootloader on /dev/sda1 (EFI system partition). Install completes perfectly.
Reboot into BIOS UEFI shell, files exist in fs0:\EFI\ubuntu, SSD still not recognised as bootable. Tried setting UEFI+Legacy Boot, still not recognised, but calling fs0:\EFI\ubuntu\grubx64.efi or shimx64.efi results in system booting, but without GRUB selection menu. Checking /etc/fstab and the EFI system partition, this time the UUIDs match, which should apparently be 70D6-1701. Not sure how this got screwed up the last time, nor how the boot files didn't get copied to the EFI system partition (probably because the UUID mismatch), but at least that's fixed.
Anyway, I'm confident that this is as clean an install as one could possible achieve, yet UEFI boot is not working properly, because if the BIOS doesn't recognise the SSD or HDD as a bootable device, it's just not ever going to look for a bootloader.
As far as Windows 7 is concerned, I followed Microsoft's advice to boot the Windows 7 Installer directly from the BIOS UEFI shell, but it still locks up at "Starting Windows". I'm pretty well convinced these problems are related.