You ask, “if I had blown as hard as I could right from the start of the test is it likely my FEV1 would have been higher?” Three factors come into play. First, the effort must be forceful but smooth; not a sudden “grunting” of air. Second- with proper technique there is an upper limit to air flow, beyond which further effort does not heighten flow and may actually distort overall (7-8 second) flow. Another way to put this is that optimum effort should cause a perceived smoothness of flow rather than a bearing-down jerkiness of flow. So the answer to your question is, maybe.
You state that, “most of my FEV1 readings are in the 1.85-2.25 range and have only had a very few that were in the 2.40-2.50 range, which are all well below the FEV1 shown on the spirometry shown above.” That is not quite the case even if you weren’t having a very good day on the day of the Spirometry. That is because for all practical purposes normal variation in flow rate can vary more than you might expect on a day to day basis, 2.25 -2.50 being very common; 2.10-2.50, less common but still within the range of normality, and thus your home device measurements may be reasonably accurate.
Even if Spirometry reflects the true state of affairs, the key for monitoring is to establish your personal best on your device and interpret the significance of subsequent measurements on that device with your established personal best.
You should also discuss your questions with your lung specialist.