<human>: Can you condense the text into a few key points?

Maybe the title is not clear but the situation is as follows.

I currently work in a pretty nice job, good pay, work is fun, however I'm not happy with the career opportunities, company culture and my manager. When I got a message on LinkedIn about applying to a new job I went on a few talks at the company and have decided to go for the new opportunity.

Now things get a bit fiddly. The contract has not been signed and will not be signed until the third week of January. This is in mutual understanding and I have a spoken agreement about getting the job. However until the ink is dry, I have the mentality "prepare for the worst, hope for the best". 

My current job has a notice period of 2 months starting at the first day of the month. This is quite normal in my field and my seniority level, so nothing strange there. Quitting in January would mean I work until the last day of March. 

My current boss just dropped the bombshell that he wants me to manage a large project that I was hoping for to manage for about 6 months. Saying no would be A: A career killer, B: Make his extremely suspicious about me leaving the company, C: In case I don't sign the new contract for whatever reason pretty much ruin me within my current firm, I won't be fired, but my job and the entire atmosphere will be abysmal. 

Now starting this project would involve a ton of travel on my end, and our policy is that of "book early, and skimp on cancellation insurance". Also if I start the project and then hand it over to a colleague it would most certainly have a high change of failing.

So I am in dubio. I don't want to cause problems for the firm, I mean, for all it's flaws, they never wronged me, and actually provided for me several times. On the other hand I do not want to risk not signing with the new firm. 

Next Tuesday we will start planning for the new project and first bookings etc. will be made in the first week of January. 

How do I deal with this professionally?
<bot>: New job to be signed for, investments to be made in current firm, can't tell current firm that I am about to quick, don't want to ruin a project.