Essentially, I find the interaction of this skill and these two missions to be both incredibly convoluted and potentially very imbalanced. The rules state explicitly that if the Jumper "trooper" (which is actually several troopers, somehow) becomes the lieutenant, than the controlling player will not suffer Loss of Lieutenant unless all of the component troopers are incapacitated. It seems to imply that this Loss of Lieutenant state occurs whether or not AI Beacons remain on the table. If that's the case, does one have to kill all of the proxies (and possibly the enemy AI Beacons) to achieve a lieutenant kill, as none of the component troopers are technically the lieutenant? If that's the case, is it possible to spend your lieutenant order on a Jumper collective, as none of the troopers that can be activated by the order are technically the lieutenant either?
So the key here is, regardless of if the proxies themselves are considered troopers, you haven't nominated the proxies as your LT, you have nominated specifically the Ghost Jumper entity which is considered it's own single trooper which stands separately. With regards to Decapitation, the rules for Jumpers tell us: If all the Proxies of a G: Jumper trooper are in Isolated state, or any Null state, then the G: Jumper will be considered a casualty until at least one of his Proxies recovers from such state. So there's no issues with the wordings or technicalities there, if you want to kill the LT you need to kill and/or isolate all the proxies (technically isolating wouldn't work for most LTs, but here it does cause this LT to be a casualty). Netrods have no impact, the trooper is still a casualty, the rules there just let you continue to use the order. With regards to Hunting Party and LTs, it is admittedly a bit problematic, technically there's no way to put the Jumper entity into the isolated or immobilized states, I don't think it's game breaking for this to be the case, certain factions and units do better at certain missions, but I would suggest most players would happily treat a posthuman whose remaining proxies all satisfy the hunted down rules as itself being hunted down though. For hunting down specialists you should consider each proxy separately (it is the body which is a specialist, not the jumper entity)
Check the its question and answer thread abput posthumans and hunting party. If the rules for loss of lieutenant are not in effect, the posthuman entity cannot be chosen but a single mk proxy must be. This means in hunting party the posthuman can definantly be hunted down. This may have weird interactions with spending the LT order, but that is how its been ruled.
A post in the thread explains that this post was due to the posthuman (not proxy) is the LT when loss of LT is in effect. Decapitation doesn't use loss of LT so is ignored.
you are correct, apologies sir. That response is from a Facebook conversation I had with Mark Manlapas for how does this work at Rumble at Route 66 (In US) and not the Its 9 Questions and answer thread on WHY it worked that way (the hunting party thing came about because of this Facebook conversation i believe however). his response was: "Hell Lois has spoken: In essence, "the G:Jumper and LT" bullet is considered part of the Loss of Lieutenant rules by this mission and is ignored. Instead, you pick 1 proxy as LT, placing a marker on the table if that proxy was in Hidden Deployment. For Hunting Party, only that Proxy is considered your LT." However, this is me saying, what another person said about what Hell Lois said about how this works. This is not a valid source and take it how you will. That said it is valid for me going to Rumble and moving forward it seems rather balanced response. But a valid source that you can use to convince your meta it is not.