Unfortunately, engraves cannot be placed as far over to the right and left sides as cuts can - the head requires additional deceleration space for the side-to-side movements - so that is why the engraving probably didn’t print for that one coaster - it was too close to the right hand limit. (See how it is grayed out in the preview up top? That means it will not engrave. You want engraves to show up as pink.)
For the cut on that coaster - there have been a few issues with shifting on cuts placed in the lower right hand side on a few machines. Sadly, it sometimes requires replacing the machine, but you’re going to need to hear from support to verify that there is a problem with it.
What you can do to test for them and save yourself some communicating time, is open up and print the “Gift of Good Measure” on the sheet of spare Draftboard that they sent for testing purposes - place the print in approximately that spot on the board, but make sure that it is within the printable area. (Not overlapping the gray no-cut zone.)
Then take pictures and post the results here, along with the time and time zone of the test. You can also turn off the machine and slowly move the print head all the way to the left, and all the way to the right along the gantry, to see if it hangs up on anything, then forward and back along the right side. Then tell them your results.
Hope it winds up being nothing. Fingers crossed.