Can the systolic reading on a home bp machine fluctuate 15 or more points in a single sitting (taking bp three times)? or is my machine likely faulty?

Entirely possible: Be sure you're at complete rest for 10 minutes before starting and stay at rest while you make your measurements. If each successive measurement falls, you likely have anxiety related (anticipatory) HTN and the more you measure it, the less this will be an issue as you get more used to the routine. Meanwhile, measure 5 times, throw out the low and high, and average the other 3.