It is reasonable to expect a contractor to replace the last foot of HVAC duct work, the connection between the insulated duct and the register

I don't see a problem with that, other than the existing duct doesn't look wide enough to fit both. You'll have to get/build a reducer that goes from something slightly wider (that can support both circular ducts coming out of it) to the existing square duct size. Most metal shops can build this sort of thing for you - I had a couple 45-degree elbows built to re-route some ducts in my basement, it cost me around $50 I think.

 | |   | |
 | |   | |    <--  existing two round ducts (one moved)
 | |   | |
+---------+
|        /
|       /    <-- new reducer
+------+
|      |
|      |     <-- existing square ducts
|      |

The main thing is to keep the number of elbows to a minimum. In fact, in your case it may work better as it looks like you'll reduce the number of elbows by one.

Another option would be to extend the main duct, and split the two round ducts off at the end. Not sure how long those are now, but the box stores carry a few regular square duct sizes you can buy and assemble/install yourself.

I would not use flexible duct in a crawl space. It is like a 4 lane freeway for animals and bugs. Rigid duct is very easy to piece together. Even long runs might take you an extra few minutes.