Convert as many citizens as possible in all your other cities into Scientists until you can research The Laser in 4 turns. This should be possible since all other considerations (city happiness, city production) are unnecessary for all your cities apart from the one you want to build the SS part.
Max out production in your target city. Sounds like you've already done this, but just make sure the city is using every tile in its radius (join workers to boost it if neeeded).
Start a pre-build straight away in your target city. This will give you much-needed production bonus. Just make sure you will finish research on The Laser before you complete the pre-build.
When you have researched The Laser start producing it in your target city.
Change you tax rate to 100% after research is over ... this will give you a lot of money so that you can try and hurry the production in the last turn if you have to.
Attack the weakest and nearest enemy Civ with every offensive unit you've got (the Elite ones take priority). If you are lucky you will create a Great Leader and your problems will be solved.

You don't have to worry about being sucked into a long war or getting your army killed because the game will only last a max of 12 turns anyway.
Hope this helps.