I'm betting money that your objectionable taste is from burnt sugar from the kettle.
Edit: This is my thought before your second burnt confirmation post. Not meaning to over state the obvious.
Let's a assume it's not at this point. The small about of smoked you used unless it's peat smoke is not over the top in its application. In fact it would be noticeable in the pour and first sips, fading with time as you drink your beer. Ones taste buds desensitizes to smoke as your pallet adjusts to it, but it's never really gone. It's the same thing with hops not to the extent that smoked fades sip to sip, beer to beer.
Aging smoked beer helps, while it doesn't fade the smoke flavor it softens other things; greeness of the beer, yeast ester, hop aroma, and any aromatics in the malt. Aging beer on co2 if it's force carbed can have a carbonic bite, that carbonic astringent character will fade within a few weeks. The smoke character can change slightly with time but don't expect it drop out of your beer.
I would do nothing with the beer but age it, it's big, give it time. Possibly six months at that ABV. You might try it serving it cooler, pick a glass with a narrow opening like some nice stem wear. Have it with food or while tending the grill/smoker. I would have one of these smoked foods, any BBQ, spicey grilled Mexican or Hot stir fried Thai. Same with snacks, Chipotle salsa, smoked salmon, smoked kippers with onions and mayo on crackers, or smoked cheese, smoked almonds, and smoked sausage with fresh pineapple. The possibilities are endless.
Some defects in beer can fade with time. I once lost steel mesh screen in a carboy only to have dissolve completely making a metallic beer. Was going to dump it in six months, cracked the first bottle, started to pour but stopped and put it into a glass. It was miraculous, no metallic taste what so ever. This was only a two gallon batch thankfully.
My guess burnt sugar is your problem with a smoke taste from that late addition. Then add your smoked malt to that taste.
Again, do nothing, let it age. Maybe you will be lucky. Bottle it in a month or so if you want that keg emptied.
Next time, add your sugar prior to boil. If you have it hot on the burner, move it off the burner, add and stir well, use your long brew spoon to check for obstructions in the bottom of the kettle, if so stir more until dissolved.
I hope waiting it out is what's needed.
