Just found this Compact Burning Bush at an Ace Hardware store and brought it home. Would it be wise to go ahead and do a chop on it so in spring it could back bud? I am thinking about a 30cm/12in tree. Rule of Thirds? 30cm tree should have 10cm trunk?

I'd personally wait until spring, but because of where you live , you may be okay. I worry about hard winters damaging my trees in dormancy, but South Cackalacky has a milder season. If you do it, do it now and not in the middle of winter. Otherwise, spring is always good.
If it were my tree, I'd cut the right branch completely, and leave the other one to grow for a while. Plant it in the ground or larger container to thicken it out some more.

Oh my gosh. I just re-read my post and realized I posted something completely wrong. The rule of the 1/3 is in regards to the canopy and branches not the trunk. The height is 6-12 times the width of the trunk. So I only need a 5cm (2inch) trunk. I don't know what was wrong with me that day. Oh no, am I getting old?