FWIW, I often shoot just 3 rounds for a chrono reading... I just need an idea of where they are at, and particularly with handgun ammos. If I'm really looking for statistical numbers, I go to 10 rounds over the chrono. I never accuracy test and chrono at the same time... just my method.
I don't know that case volume in your case really is that much of an issue, but something IS... and I understand your need to find the root cause. I have had to go so far as to throw ALL of my data out the window, and start from scratch... taking what I've learned along the way to improve my process, but incorporating the lessons learned into a new load work up. To try to break down an existing data set, looking for the needle in the haystack... or needles... can be frustrating, and often inconclusive. Also, don't sell yourself short... you mention you don't shoot well enough, yet, to make premium components worth the cost... I say bunk! I would use the components you have to get valuable trigger time behind your rifle, while at the same time refining your reloading process, meanwhile taking small but positive steps working up a competition load. I am doing the very same thing right now with my Savage 10 in .308. I've never shot a rifle that capable, nor a scope, generally. The learning curve is pretty large... and that is just pulling the trigger. I've reloaded for the .308 for years, but I'm still learning every step I take in the load workup for this rifle, and much of the process I used to load for my M1a, and cast bullets for my Savage 99... have no application here.