I have a quil-to-threadless adaptor on one of my older road bikes, and it works just fine.
I don't know that you will need one that's super-extra-long like that, especially if you're running a long, tall stem like that Delta. Keep in mind, a kicked-up BMX bar, like the Surly will put the grips up higher, so you will want a correspoindingly lower stem.


Get a stem adapter for a 1" headset >1-1/8" stem, and get a stem that has a 1-1/8 HS and 31.8mm bar clamp. These are by far the easiest to find, and 31.8 is the modern standard for both MTB and road bars, so you have a lot more choices.

Otherwise, you'll be looking for that unicorn stem that has the exact combination of dimensions (that never would have been put on the same bike) These things exist, but they're neither easy to find, or inexpensive to aquire.