1. That something is a christian idea doesnt mean it cant be a jewish idea. Afterall both christians and jews believe the jews were redeemed from egypt, that adam and chava ate from the tree, that there is reward and punishment, in a moshiach etc. Are we to say that we must throw out half of our beliefs because someone else also believes them? “Shared ideals” are allowed to occur.
2. It isnt even the case that moshiach coming from the dead is a christian concept. Yoshke was killed, resurrected 3 days later and then ascended to heaven in his body. Meanwhile, if you believe the rebbe is moshiach you either 1. believe when he resurrects in order to reveal himself or 2. is alive in this world in his kever or some hidden way. Meanwhile the christian is waiting for his descent from heaven. The resurrection for them has nothing to do with his “coming”. In fact, you should really have a question on the zohar and arizals account of moshiach that he will ascend to shamayim and come back down after a time. That is way more christian than moshiach coming from the dead. It is a curious point that in zero of the debates does a christian argue that the gemara about daniel being able to come from the dead as moshiach is a proof for the christian worldview. They always quote that moshiach was born during the chorban beis hamikdash and was taken to gan eden. The reason for this is obvious: Saying moshiach MIGHT(as the gemara says he might be from the living) be able to RESURRECT and redeem us has nothing to do with christian belief that moshiach HAS to DESCEND body and soul from heaven to redeem us.
3. It is very popular to believe that klal yisroel has had a simple universal concept of moshiach but that isnt the case. There have been all kinds of beliefs about moshiach which only get more interesting with the spread of kabbalah. Some say moshiach will resurrect, others say he will come from heaven in a body or as an angel, others say he is alive but looks dead, others say he will be enclothed in a fake body etc etc etc. Baruch Hashem jewish beliefs have much variety. Perhaps for a rationalist like rambam people being concealed in hidden worlds or resurrecting wasnt seen as anything to seriously consider, but kabbalah is now the name of the game and one must recognize these types of things are rather normal belief. Whether its the idea that Yaakov avinu had a second spiritual body which he was able to enclothe himself in after death whenever he wanted as Rabbeinu Bachya says, or whether Yitzchak died as a korban olah but magically appeared to be alive even though he was no longer in this world as the Chiddushei harim says, the jewishness of these mind boggling ideas predates contemporary jewish messianic movements.
4. Why not dovid hamelech? Well if you are a messianist who says the rebbe is chezkas moshiach that means he has a chazaka that he has started the process, why, if you think someone is in the middle of the process would the conversation be open to someone who isnt in the middle of the process? Thats a misplaced response. But if you say you are a messianist who just believes his rebbe will be the one who is chosen over dovid hamelech even though it is technically halachically possible it could be dovid hamelech or someone else, they have on whom to rely. Other tzaddikim of the past continued to believe their rebbe would be moshiach(like the ruzhiner or the baal shem tov) after their passing over other people. If someone thinks that the rebbe is more fitting since he kuched in moshiach he is entitled to have those preferences. There are in fact people who say that this was the reason daniel is considered in the bavli as he prayed for the beis hamikdash and as a reward he should be moshiach who builds the third. A lubavitcher may want to argue amonst these lines.
5. At the end of the day many talmidei chachamim allow for the possibility of moshiach coming from the dead, and many dont. Its a machlokes like any other machlokes like shaving, cholov yisroel or what have you. But as R Dovid Cohen said a few years back on dovid lichtensteins show “its not a pesul at all” “throughout the ages there have been people with this kind of hashkafa”. Enough said