I have been answering a few questions behind the scenes.... Smoking Don is welcome to share if he wishes.
Kevin gave me a few ideas then I ask him about using a mop, these are the ideas he shared with me and I will pretty much go with them. His goat burgers and the seasoning at the Ohio gathering was delicious!
Stalag, (Kevin’s) ideas on fixing goat
seasoning is to taste. I prefer cumin, garlic, black pepper, cayenne pepper, thyme, and if you have it some dill. If roasting I surround with carrots, onions, and Celery. I use noniodized salt on all meats. If you are smoking, I would suggest that you consider adding a little brown sugar into a rub made from garlic (smashed or powder, onion (fine diced or dried or powdered), cayenne pepper, Celery salt, cumin, and thyme with olive oil to bind the rub together a bit. Goat is a strong tasting meat so go strong on the pepper and cumin. The thyme if added in the right amount offsets the cumin a bit. I do not have exact amounts as I would do to taste. What I suggest should also work for lamb or grass fed beef that has a stronger flavor than corn fed beef.
I would avoid the brine, but use instead some sea salt in the mix of spices. The mop of butter, apple cider, and lemon sounds good. However I think the mop might overdo it. If you do go to roasting, the roast should be covered and the added wine would be more than sufficient. Goat is strong enough in flavor that you could use a dry red cooking wine and it would do well with the pairing. Cook with the fat side up low and slow as well. Goat tends to be tough and will need gentle cooking to make it tender. If the fat content is low, the only reason I would do the mop you suggested. I would first add salt, cayenne pepper, and black pepper to the smoking portion (mop here if you wish), then when you switch to the roast, add the garlic, cumin, thyme, rosemary, white pepper spices with plenty of celery, carrots, onions surrounding the roast in the roasting pan, add the cooking wine and a little of the mop, cover and continue the cook low and slow until you reach an internal temperature of 160. Key is low and slow! I recommend on the roasting portion a temperature of 250.