I know you don't want to buy another tool, but now is the time to do it.
For making crosscuts on a long board, I use and recommend an ordinary circular saw. I clamp a straight scrap board across the board to be cut, square it and line it up. I use the board to guide the circular saw, by pressing the side of the saw's baseplate against the edge of the board. Arrange the guide board and orient the saw so that they have the maximum support from the board being cut.
You can do the same thing with the jigsaw in theory, but the cut won't be very clean. A circular saw will give you a neat, straight, square cut.
If you do not own a circular saw, borrow one from your neighbor or buy one for under $50. Harbor Freight sells one for less than $30. That is $10 per cut, and you get to keep the saw. You will find lots of future uses for a circular saw, too. For the crosscuts, you will also need two clamps and a straight board.