OK, some things here are now clearer, and some are now murkier? Let's divide up your statements from the last post.
Max PV Array Open Circuit Voltage @145Vdc
OK, it appears that I was looking at the specifications of another inverter if yours has a Voc of 145VDC. So, that makes sense now that only three panels can be wired in series. Here are the specs for your panel (I think). With a Voc of 136V, three in series barely is under the 145V cutoff. I would be very concerned about cold weather. As the temperature goes down, the voltage goes up, so in winter, just as you get to freezing, the Voc will >150Voc. Use this string calculator to determine what your winter lows will be like.
https://www.midnitesolar.com/sizingTool/index.php You are so close to the Voc limit that you might have to drop down to just two panels in series, depending on your weather.
I read the startup wattage on the inverter display, when my wife turned the pump on for me.
No, this might be inadequate. The inverter display, or even a regular clamp meter is not fast enough to read the inrush current of a starting motor. You need a clamp meter designed to read "inrush current". The one I'm using right now is a Uni-T 216C. But, since your measured readings of 0.8 kW and 2.3 kW jibe with my inrush readings, maybe your display is fast enough.
L1/L2 are on 40 amp bipole breaker back feeding my distribution panel
This sounds like you have a standard split-phase electrical distribution panel if you are using a dual-pole breaker to get 240VAC. For all the single-pole breakers on L1, does there appear to be an empty space right next to them, or are they snuggled against each other in the panel? If it is a split-phase panel as I think it might be, then all the empty spaces are L2 circuits. Pics here would help! All this could be verified in seconds with a voltmeter set to read AC volts.
The pump is just plugged in to a regular 120VAC outlet in an equipment shed
OK, this is very confusing? Is this supposed to be a 240VAC pump or a 120VAC pump? Does the pump actually work at 120VAC? Does it run half as fast as it normally does? If it has a standard 120VAC plug wired to it, and you have it plugged into a 120VAC socket, why were you trying to run it at 240V? Does it have some kind of dual-voltage motor?