I would make the "X" with a lap joint in the middle, then trim to fit, taking very light cuts as I get close.
* Table saw to make the lap joint.
* Miter saw to trim the ends of the arms to fit.
* Make the "X" oversize. On the table saw, cut and press fit the lap joint, but do not glue it. (Let us know if you need instructions for making a lap joint.)
* Find the exact center of the "X" in the middle of the lap joint and mark the spot.
* Mark a centering line at the end of each arm. The line should go down the middle, parallel to each arm.
* Mark a spot near the end of each arm on the centering line, close to where the corner should be. The spots must be the same distance from the center mark, and slightly "inside the square hole." You will use these spots to center the "X" in the square hole for marking.
* Mark a number (1, 2, 3, 4) on each arm so you remember which is which. (When you are trimming the arms to fit, you don't want to keep trimming the same arm by accident.)
* Hold the "X" against the outside of the square hole with the marks facing in. From the inside, line up the centering lines on the corners of the square hole. Adjust the spots on the lines so that they are the same distance from the corners, thus centering the "X" in the hole. Ask a friend to hold the "X" while you make the marks. It would help to have a light under the table while you work.
* Use the edges of the square hole to mark the corners near where the "cuts" will go on the "X". The marks should be 45 degrees and come to a point on the centering line.
* Before making the cuts, check your work to make sure the "X" is centered by measuring from the cut marks to the center spot. They should all be the same distance.
* Cut outside the marks, so that the "X" is slightly too large. Leave yourself room for trimming.
* Reassemble the "X" and test the fit carefully. Trim the corners a tiny bit at a time on a miter saw, reassembling and retesting each time. Trim the four arms evenly, so that the point of each arm stays on the centering line and the distance from each point to the center stays equal. Test after every cut; don't be tempted to make multiple cuts and then test. Keep taking tiny bites and testing the fit until it is perfect. Remember: You can always cut off, but you can't "cut on."
* Clamp and glue the lap joint.
* Sand off the marks and finish to match.
How will you attach the "X" to the frame? Press fit and glue?