No need to worry, as far as I know this does not send suckers up from the finer roots. the sbk drilled into the main root should be fine as just one application. keep the bag on it for about a week, this allows the sbk to be absorbed and the surface of it to dry.

Chop off all the main plant from it's roots. You've got a job on clearing the stuff that's already climbed!
Wait till it sprouts & grows new leaves again, the tender young leaves will take systemic weedkiller to the roots most effectively. You can bruise the new growth to make it more susceptible.
As an aid to avoid 'overspray', in windy conditions, cut a 4 pint plastic milk container in half across the middle, put the open bottom over the plant & spray the herbicide through the pouring bit

Agree with Seaburngirl - if the main root/s are under where the new deck will be with a bit of clearance between soil and deck beneath, treat with SBK as previously described (neat) and either put an upturned pot/s over the treated bits and push the soil back, or use plastic bags to cover and then replace the soil and level off.. And just build your deck as soon as you like, leaving the pots or bags in place; if you wait for signs of possible regrowth,that won't show itself till next year in spring or summer, so just be sure you've managed to get out most of the roots by digging as deep and wide as necessary, and have treated (with SBK) any remaining large,woody roots properly,especially where it goes under next door's fence. Buy a large bottle of SBK, not the 125ml one! How deep and wide you need to dig is impossible to say - all that can be said is, after 10 years, it will have an extensive root system - large roots tend to go down deep for anchoring purposes, and smaller roots may spread far and wide; fibrous roots are usually headed towards anywhere that does not consistently dry out. ,Assuming there's clearance between the soil and the new deck, covering the soil with a heavy duty weed membrane pegged down round the edges prior to construction is a wise move...

Any roots left outside of the deck area should be treated in the same way, but they're obviously not such a problem to retreat next year if necessary.

Thank you all for your very kind and thorough help. I wish I could return the favour somehow :)
Will keep you updated if you are interested!

I think you're going to need all your energy and discipline to complete a rigorous uncovering of roots! Good luck with it... be nice to hear your progress and to see photos of the deck when its done...

Hi.
I'm in exactly the same boat.
How did you get on?
Did it ever grow back?
Thanks in advance,
Dave

Hi Dave,
We followed the advice given here and it never returned: we used SBK on the drilled roots that were going into neighbouring land and everything on our property was dug up slowly over a period of 6 weeks, this time of year before winter kicked in actually (soft ground). I was very thorough, leaving no root at all and it had gone a long way, about 5 meters in some directions. The roots that were going next door were given SbK and wrapped in plastic and elastic band and I placed a visual cue to remember where they were so that I could quickly check once a month in the following 2 summers - between March and October.
There was one shoot going under our summer house concrete slab though, which was worrying: same treatment and I placed a plastic barrier into the ground to try and smother it of light and water. It could still return... We will have to continue monitoring once a month for another few years.
Good luck.