I must say you are going for the top-o'-the-line crank. The FC-M980 is a "Hollowtech II" crank and has the spindle built into the drive-side crank arm so you need an external bearing Shimano bottom bracket. The correct one is Shimano's SM-BB93, English threaded.
You will need the installation tool to match the cup's splines and the Park Tools BBT-49 is one. However, that bottom bracket includes an adapter to let you use the same installation tools used for the previous Shimano road and MTB external cup bottom brackets such as the BB-6700, BB-5700, etc.
However, if your bike currently has the LP-27E bottom bracket you note, the "E" means the front derailleur is mounted on a ring that is held in place by the driveside bottom bracket cup. I'm not sure if the XTR bottom bracket is suitable for that use but I believe it will work as it's suitable for both 68 mm and 73 mm bottom bracket shells so the drive side spacer can be replaced with the front derailleur's E-ring.
You will need different tools to remove the current crank and bottom bracket and that's probably best left to the bike shop since it should be a one-time job and not worth buying the tools.