There is no reason you can't request the salary desired and the reduction of the notice period in order to accept the promotion. Explain, in a professional manner, that you would require X salary to accept the role and that you find the extended notice period to be unacceptable since it effectively seeks to curtail (or at least hamper), your career and future employment prospects.
You don't need to explain or justify your salary request - although obviously if you can show it is in line with industry standards and further support your claim with examples of the work you have done to deserve it, you have a greater chance of success. Equally you don't need to mention you're already on the lookout for a new role - long notice periods can be considered unreasonable even by people who love their job and never intend to leave.
If your employer is unable to meet your request you can decline the promotion. There is more to life and work than salary and titles. Its perfectly acceptable to say something like "I appreciate and am honoured by your offer and the faith you have shown in me, however I'm afraid, in this instance, I don't feel this is the right move at the right time for me career-wise".
Your boss may read between the lines and see he/she needs to meet your conditions of they want to keep you. Otherwise, everything goes on as normal.
Nothing unprofessional or underhand about any aspect of it. This is just business - you need to do what's best for you and get the best deal you can.