for all that it will cost you and what you plan to use the car for i would not do it. this is coming from someone who has put a LS unit into a non-M diff many years ago.
i absolutely loved my LSD but for the cost and effort that you say you want the car for i would pass.
also as said, the M5 diff is not what you need
OE CSL WHEELS - OE CSL BRAKES - OE AUTOFOLD MIRRORS - CSL TRUNK - CSL DIFFUSER - AA SPORT TUNE - AA PULLEYS - BILSTEIN PSS9s - AS 40% SSK
CF CSL RACE LIP - NAVI - BMW PERF CF STRUT BAR - BMW GROUP N MNTS - GRUPPE M CF INTAKE - UUC SS BRAKELINES, TRANS MNTS, RTABs - 4.10 BMW M-SPORT DIFF