You are not alone. BI is a double edge sword for many casual users; it has lots of power and flexibility that comes with a steeper learning curve. I was already up to speed on other BI knowledge, then had to put in about a full days worth of reading/experimenting before I got to where I am now... AI almost half way figured out, hehe.
Before reading on, first I recommend opening the BI AI toolbox (BI status button/AI tab), then double click on some alert that was cancelled by your existing settings. What happened to cause the cancellation will now be displayed in detail the toolbox window. The image will show clearly what your AI looked at, and how well each step in the process went. Once you've absorbed that, you can use the AI toolbox again later and see the affects of some adjustments I'm about to recommend.
Zone A is somewhat narrow, and the way you have everything setup BI is likely to send images to AI that have the logos blacked out. This is a perfect case to use the "zone g workaround" I mentioned above. In your zone setup, leave zone A as is. Change zone G cover the entire image, then save. Next go to your camera AI settings, where you have zones G and H disabled, and enable the G checkbox. These settings will make it where BI always sends complete frames to AI, logos and all (no blacked out pixels).
Now you probably don't want to add zone g to motion triggers. In the cameras object detection settings, you have "object crosses zones" unchecked. That means movement >100pixels in the substream on ANY zone will trigger, now including zone g. To fix this, you have to enable the "object crosses zones" checkox, and enter "A" in the list. This way BI will ignore motion in any zone except A.
Next, you mentioned you only want to confirm logos when the vehicle is stopped in zone A right? If that's the case, in your motion settings, try enabling the "OPPOSITE sense to detect non-motion" checkbox. Again, I haven't played with this myself, but guessing it's what you are after. If that tree could cast a moving shadow on the side of a stopped delivery van, you will probably have some added complexities to deal with (in BI motion triggers and zones setup). This setting may also interact with my next setting?... not sure but logic tells me pixels traveled before motion stops could be relevant? [edit: On a sidenote, I don't see a street side mailbox. If you just want to know when you actually get deliveries, you could instead trigger the clone on the walkway. It can still confirm the logo on the van for alerts, assuming the delivery person that triggered it is parked in view. This could give you the same result but with less processing for each passing vehicle.]
Lastly, you have the setting "object travels 100 pixels in substream". I believe 0.3mp is D1 resolution, or 740x480 pixels (roughly?). Eyeballing scaling this, your zone a looks roughly 400x100 substream pixels or so? Depending how well the camera sees the lower part of the truck etc, 'object center point traveling 100pixels' may be unreliable (oops, they left out 'center point' didn't they?). With certain lighting conditions, colors, reflections, etc... the apparent center point of motion can end up being all over the map. I would drop that to 60pixels to make it more sensitive to ensure you don't miss anything; AI should filter any false triggers anyways.
The rest of your settings look like they should work fine for what you want.
Best of luck... if it encourages you at all, mine hasn't missed a single one out of the last 20.. including very different looking garbage/recycling trucks... no video card just intel 4500k w/ intel beta HA w/ 6x 2-4mp cams. Cpai and delivery.pt is awesome!