My thoughts....
What is the significance of Clarinet B+ from the 5V secondary center tap?
It is basically the same point as pin 8 or pin 2
What's happening electrically and how is it better/different from the conventional way of coming off pin 8 of the rectifier?
Difference if any should be negligible. You can connect it to pin 2 also.
If one didn't mind the expense, would a conventional B+ voltage from the rectifier with an CLC filter be better, or just different and more expensive?
Of course, it is better ripple measurements wise, because of additional filtering. But probably not necessary in this case as per design. If needed, to reduce hum, then for sure Jim included that in the circuit already.