The only issue is around high sugar content of rubs and in the sauces.
Some of the sweeteners (eg Maple Syrup, Molasses etc) used can spike you but my advice is test
As a T2 you may not get prescribed a meter (sadly you cannot get a Meater on NHS) but invest in one.
Test every food you eat and see what spikes you as some foods will be okay (less than 2 points higher than pre-meal after 2 hours) and some will remain higher (avoid)
As with everything - in moderation you will be okay. I ate really badly over the summer but my test still showed up as fine. Back into it now (its hard - but don't give up)
1500 cal per day is achievable
Outside of BBQ, try Livlife bread (3.8g carbs per slice instead of about 20 for normal bread) or go for Hovis Lower Carb
There are also loads of lowcarb wraps, rices, noodles etc - and swap out certain brands of fizzy drink for lower carb equivalent. Try cashew butter and eat cheese as a snack
Hope this helps