if the rubber boot is present and in good condition there should be no problem with leakage with any "self leveling" grease like Cornhead Grease - I've always used a moly grease and it works fine sticking to the metal in extreme heat applications, the parts don't move far or fast but it can get hot next to the engine .... also, contrary to the wording of the manual, I wouldn't "fill" the box with grease
Bill