Forgot the chicken advice: Your method sounds fine. Just wanted to contribute a recipe. I have served this dozens of times to rave reviews. Lime Marinated Grilled Chicken – Recipe File – Cooking For Engineers
On a standard gas grill set to medium, I’d say cook breasts 7 min a side and thighs/drumsticks 12 min a side. Note that despite the chiles it is not a spicy recipe. If you like it hot, add a shitload of cayenne pepper to the rub (like at least 1 Tsb) and/or just provide hot sauce. The marinade provides chile flavor but no heat.
Also remember to adjust the rub and marinade to the amount of chicken involved. – Docjowles
Cut the limes in half (to prepare for juicing) and mince the garlic and chile pepper. Pour the salt into a large measuring cup and add enough water to make four cups (about 1 liter). Stir the salt water until the salt has dissolved. This is also a good time to prepare the chicken. The marinade will be enough for two whole chickens (cut up) or 8 pounds of drumsticks (my favorite). Put all the chicken in a large resealable plastic bag. I called this mixture a marinade instead of a brine because not only does the solution include salt, but also acid (lime juice). A soaking solution with acid should be referred to as a marinade.
Juice three of the lime halves (using a juice extractor or a reamer) and add the juice to the salt water. Add the minced garlic and chile. Stir once to mix. Pour this into the plastic bag and reseal the bag. Try to make sure all the chicken is submerged in the marinade. With a fairly full bag, you may need to squeeze out almost all the air to accomplish this. Place the bag in a container and place in the refrigerator for at least one hour. Two hours is best, but any longer, and the chicken may become too salty. (The minimum ingredients in this marinade are the water, salt, and lime juice. The garlic and chile can be omitted if you don't have them handy.)
After the two hours, preheat your grill and remove the chicken from the refrigerator and take each piece out of the plastic bag and rinse it off in the sink. If you don't rinse the chicken off, then the salt water lingering on the surface will make the chicken too salty.
For seasoning the surface of the chicken, combine 1 tablespoon paprika, 1 tsp. onion powder, 1 tsp. ground coriander seed, and 1 tsp. garlic powder. Feel free to try different spice and herb combinations to fit your taste.
Toss the chicken with 1 Tbs. olive oil, the juice from the remaining half lime, and the seasonings prepared in the previous step. Using your hands to mix the chicken with the seasonings is the fastest way I know of to get an even distribution.
Place the chicken pieces on the grill, being careful not to crowd the pieces. Grill, turning every five minutes, until white meat reaches 165°F - 170°F and dark meat reaches 175°F.
Remove the chicken from the grill and let stand for five minutes before serving.