If there was no bco, the question I'd ask myself is " can this go on fire due to being hot"?
Timber being obviously a combustible material creates confusion.
If it is completely enclosed so that flame can't reach it, and there is no oxygen supply, then it cannot burn.
But the risk is of someone damaging or penetrating the protective boarding.
The insulated plasterboard is a great concern though. It will fail purely through heat,and then maybe some air can get in. Or eps of pir at a joint might be exposed directly.
I think you must remove that area of insulation. The effect on insulation is minimal.
BUT it is a BCO matter so you not only should do it but must do it. And most bcos I've discussed it with think timber burns even when encased, so perhaps change the timber to something else too, just within the zone distance stated.
Metal stud? Multiple layers of cement board?
If you must regain the insulation then squeeze in some rockwool if you can.
Then you can relax in front of the fire.
NB new burners have direct air intake from outside. Yours probably doesn't have that facility so will fail regs.