IMO a reliable number is not possible.
Although I can give you some numbers from my HR monitor:
~15min of swings -> 200-250cal
~20min -> 250-300cal
~25min -> 300-350cal
~30min -> 350-400cal
My data on TGUs (done in under 10mins + I've only tracked 3 sessions) shows 125-175cal.
Add another 50cal for the warm-up.
So a total session can range from 425-625cal, depending on length and intensity.
Keep in mind that the HR monitors are far from being precise.
If I were you, I'd just log a session as 300cal and be done with it.