This being a single throw DST rather than double throw as per a Shiloh complicates matters at least for me.  Once set the only way to drop the hammer (after unloading) is to tickle the front trigger and "catch the hammer as it falls.  I don't want to dry fire and drop it on an empty chamber.  More often than not my efforts result in the hammer dropping into the safety notch which, in my experience, is not a good place to be dry firing triggers.

Am I missing a trick here?

Would be surprised if the Uberti has a single lever set trigger as sometimes seen on ML rifles. They are a pain in the kozootie. Agree with Old-Win. Check to see what you have and maybe something is hanging.
Chuck

On all the Uberti rifles I have handled, and the ones I own
The DST triggers only work as a set trigger...in other words the front trigger only releases the hammer when the rear trigger is set
to uncock the hammer, with the triggers Not Set...hold the hammer and push the rear trigger forward..this works with all DST
My Uberti does not go to full cock on closing
It is best not to get into the habit of cocking the triggers before cocking the hammer...results in the dilemma above

Never messed with Uberti triggers, so may be talking through my hat. With single lever triggers, you can sometimes extend the tang on the front trigger (the part that rides on the tiny center adjustment screw) until it will lift the lever on the rear trigger enough to engage the sear and clear the notch in the hammer. Usually not enough leverage to fire the gun easily unset, but enough to disengage the sear and let the hammer down if you first take the strain off the sear with your thumb on the hammer. Triggers work normally when set.
Chuck