Without seeing the file, you might have too many nodes or misplaced nodes at the corners which can cause a problem with the angles. You talk about the speed you are using but not the force. You might be able to cut it at a much higher speed once the cuts are cleaned up, assuming that is part of the problem. As many of us have said before, if you have tight sharp corners, you can get much cleaner cuts by zooming in and moving your nodes so you have a slightly curved edge rather than a sharp one. Zoomed in you can see the curve, but when you zoom out is isn't noticeable to the eye, but the machine will handle it much better. You may also need to increase your force slightly to get cleaner cuts and be sure the card stock is well brayered onto the mat.
You have only had your machine for a week, and you are tackling a lot while learning a new machine. That is why you will constantly encourage prospective buyers to not buy the machine with a deadline looming as that can certainly increase your frustration while you are learning. Hopefully after this job you will be able to give yourself some time to experiment more. In the meantime, we are all happy to try to help as best we can.
And these machines are designed to cut very well at faster speeds and usually does quite well with card stock weighted as yours - so my guess is that you could speed up the cut - again try it on a similar cardstock to be sure you get a good clean cut (don't want you to waste card stock that you need), be sure the card stock is WELL brayered down in all areas and that no little pieces are clinging to the blade, and see if you need to at least simplify the nodes.
I am sure others will have suggestions as well - good luck. You can do it!