Well, if you have a multi-million dollar lab setup at work, you should understand the chemistry involved, or at least realize you should listen to people who understand the chemistry. I work in a lab myself, and although we don't have a multi-million dollar ISO-certified setup, I know that certain test kits for home use can be accurate and repeatable enough to give reliable results for pool maintenance. Considering this website has been helping many people with good results, I'd say the test kits they recommend fall in that category. Plus, they understand the chemistry they're talking about well enough.
Now, for your specific problem, it sounds pretty much what I had a few weeks ago. Vacuum the pool, a day later after circulating through the filter, settled 'stuff' in the middle of the pool. Water balance was ok, but FC might have been a bit too low at times.
When the weather got better, I decided to do a deep clean on my filter, bring up the FC to recommended levels and kept them there. Brushed walls and floor, scrubbed in all little areas, vacuumed. 48 hours later, the debris didn't come back. My pool's been clear for two weeks now, just by keeping up the FC levels and brushing once in a while. Before that, I was in the same situation as you.
So yes, TFP methods work, and taking samples to work will get old really fast. Especially during the weekend. Having a reliable little test setup at home really helps, and you can always take a sample to work for a sanity check once in a while. Keep your FC up, brush everywhere and do a SLAM if the stuff doesn't clear in a few days.