Firmware update stalled ... during Mojave installation

SOLVED. Thanks to all for their suggestions, as it lead me to think things through and come up with a solution. I am writing this up in some detail below to help those in the future who may be faced with a similar issue.

I decided to do a clean install of High Sierra (with USB key) onto a freshly erased HD. Once the installation was completed, I rebooted to the desktop. I then ignored the prompt to update HS and downloaded Mojave from the App Store. The install started for Mojave and as expected, and window opened and I was prompted to do a firmware upgrade. I clicked on the "Shut Down" button within the window and a secondary window opened (a beachball appeared - this is normal behaviour) and I was prompted for my admin password in order to install "Add Helper" (this also is normal). After entering the admin password, and following the onscreen instructions (I took a photo with my iPhone of the instructions on-screen for handy reference during the upcoming firmware update), I clicked "Shut Down" again within the firmware upgrade window and immediately, the screen went black and the Mac Pro turned itself off (Note: I did not manually shut down the system myself). I waited about 10 seconds (read this somewhere during my research to solve this issue and it would'nt hurt to do this) then pressed the start button and held it, as instructed in the firmware update instructions . The light flashed - I continued pushing the power button - a long beep was heard and this time, the two optical trays popped open (a visual clue that the firmware is updating itself) and after a couple of minutes, the system restarted and I found myself back on my desktop. I immediately stopped the Mojave install (in order to check that the firmware had updated itself), and held Option (key)-About this Mac to confirm that the firmware had updated itself. The firmware had updated itself from Boot ROM version MP51,0089.B00 to 144.0.0.0.0.

Up to this point, I had almost given up after multiple tries to get the firmware to update - but the clean install (HS only, nothing else on the spare drive) and then going immediately to a Mojave download worked.

Thank you for your reply Kappy. I am pretty sure that I am using the full installer - I checked the size of the app in applications and it is 5.56 Gb. However, I did find the small install file also (App Store download) also in the apps folder. I will delete the install file, just to make sure.

Hello again Old Toad. I did a safe mode boot, but am still getting that endless "click on shut down - helper window prompt - no shutdown and the helper window pops up again" loop. I have tried simply shutting down from the Shut Down menu, holding the power button to see the flashing light and the long beep on reboot, but I end up back at the same point in the process with the installation. If I recall correctly, when a firmware update takes place, both the optical drive trays should open. Would you have any further suggestions? Thank you for your time, I do very much appreciate.

Thanks Old Toad. I will try that and see what happens.

Thank you rcosta887. That is the link that I have been referencing as I try to figure this out. Much appreciated and further suggestions very welcome :-)