As noted by johnny depp the installer app should be able to see the USB drive under Windows to write the LE image directly to the SSD. RPi images do not boot into an installer where you pick the install target (as in the Generic image).
Does the SSD have it's own PSU or are you trying to power the SSD from the board? .. and what PSU is being used?. Note that USB booting has a much higher current draw on the board than SD card and will need something like the official Raspberry Pi PSU that's rated for (and will actually give) 5V/3A to avoid power brown-out issues; which from the description of boot failures and reboots is my guess/hunch on the problem. You might also need config.txt changes to boost power on the USB ports and some USB drives still suck enough current to need their own independent PSU. For kicks, you can also boot an LE12 nightly from SD card and ensure any available firmware updates have been applied (via updates in LE settings).
If this all sounds fiddly, please remember the board was designed to boot easily from SD card (and that bit works easily and as advertised). If you want to go off-piste with more exotic boot scenarios it's not quite as straightforward.