Your place and your plan sounds great.I guess I am fully willing to accept that you are reading the meter right. That said, there simply is not a 115V 1HP pump that only draws 8A. So I would say you are more likely to have a 1/2 hp pump. Try looking around on the web for how much current a 1HP, 115V single phase pump draws. I think you'll see my point.
you measure them really with a carbon pile load tester .. batteries can be funny .. but the bottom line in your case is you shouldnt try to run a 1000+w load on batteries .. hate to scold you, but what we're doing is 'solar' power .. not battery power .. if you want a 'battery' system visit the local battery supply shop and invest in about 10 grand worth of batteries, make a huge bank, and get the shop charger from hell to keep them charged, what do you want with 'solar'? ... if you do want to have a solar system re-think your approach ...for example if you could fill a large tank during the day with your pump you could feed it to your house ect with a 12v rv pump that pulls about 30 watts ...
I just was re-reading the original post. If this is really a 1hp pump, I think the OP's numbers are wrong. The rule of thumb is that for 120V single-phase, it's about 14-16A per HP. He says the current is 8A, but that can't be for a 1HP pump. If we assume an optimistic 14A and ignore the power factor, that's 120V * 14A = 1680W. If we assume an 85% efficiency for his inverter, the draw while the pump is running should be 1680 / 0.85 / 24 = 82A which is quite a bit. He's doing this for 10 minutes, which is a fairly long time for that big of a load. I guess I'm not surprised it pulls down the battery voltage like he says, independent of how good his batteries are.My 1/2 HP well pump only runs for 2-3 minutes each time it fills the pressure tank, and when it is running (with virtually no other loads) my inverter indicates about 1,000W.