I think taking the whole nose off would be easier and faster than just the core support...and its SO much easier working on the engine with nothing in your way..you'll need two people or some type of hoist to lift the nose off it,I have done it alone but I'll admit it was a struggle,using my engine hoist...I left the hood on and closed ,after taking the battery out of the tray,the fuse box wiring off,and all the little do-dads like the wiper fluid bottle & hoses,etc..Used a 2" ratchet strap around the hood and under the fender wheel arches to lift it off..
I have never used poly motor or tranny mounts,but I know others who have,and I'd reccomend you go with ALL poly,or none...I know a guy who snapped the tailhousing off his Camaro's tranny after installing poly motor mounts...they are pretty rigid,and if you dont replace them all,the OEM rubber one will let things flex enough to possibly do harm..others here who have used them will probably agree with me ..