Hi there informatics,
Just chiming in about that unfinished job they did. It’s impractical to try to get the flooring under the threshold, as the “transition” you mentioned is the nose of the threshold and attached to it. They could have at least used a 1/4 round nailed to the nose. Leaving it unfinished like that, allows dirt and pebbles to eventually work their way under your planks. Plus it just doesn’t look right. I might ask them to finish their work; “Is it supposed to look like that?” They should be embarrassed!
I made a custom, two inch wide ramp for my threshold which is just like yours. It was extra work but it was fun and it looks great. The ramp is stuck to the subfloor with a few little dabs of Loc-Tite PL3. The plank runs under it about 3/4″ and there’s a 1/4″ gap for the planks. This keeps the dirt and pebbles out from under my planks! I probably should have stained the nose to try and match it with the ramp but the color would always be “off” so I’m currently satisfied with it. Maybe another day.
You can imagine some possibilities with this photo, I think. You can even find some nice, stain-able oak pieces already cut in a similar manner, at stores like the one with the big orange sign. Hope this helps.