Low fuel economy - what else in this section

Well, none of you are assuming anything or taking for granted that I have already taken the most common steps, which is a good thing because sometimes you do forget things.

So, yes I have reset the consumption several times, usually after at least 200 miles to get some idea of what's going on. It's now sitting at 31.7 which is where it generally hovers at.
My hybrid battery did throw a code when tested last week, I don't remember what it was exactly but on the internet it meant replace hybrid battery.
My 12 volt did not throw a code but doing the test on it showed it was below 11.7 volts at start. And the multiple lights on the dash went away when I replaced it. The battery was 5 years old.
The air in my Tires was checked and my tires rotated as well two weeks ago by Discount Tires. One of my tires showed unusual but even tread wear and was replaced. I have an appointment to get my alignment checked. I have it done every 6 months.
The engine swap did not affect the MPG.

The circumstances that resulted in my loss of mpg from about 40 mpg to about 31 mpg was this:
I went to get an oil change at Walmart. While waiting I got a text message they could not start my car. They had inserted the keyless entry fob in it's holder, something I never do, and the car would not start and showed no power. We called AAA and the guy said we tripped the alarm and that cut the power but he knew how to reset it and also said the 12 volt battery was very low. I went and got it replaced however the one I got also was bad. I got a refund and put in an AC Delco which lasted a few months. It too was barely hitting 12 so I checked this forum and from the recommendations bought an Optima which lasted 5 years.
Ever since the above incident I have never regained the higher mpg and have been near the lower end of 30 mpg.

 

So I was driving tonight on the freeway and I was accelerating and my battery bars went to zero and my dash lit up like a Christmas tree again (see picture). I was able to get home no problem and by the time I did my battery was charged up about 5 bars. I did a check on the 12 volt and it read 12.7 and 12.4 in acc mode. Since I replaced the 12 volt battery and the traction battery and it's doing the same thing, the only thing I can think of is the inverter now. Is this the most likely culprit?
I checked and got these codes:
P0A80
P3000

 

I think your right, I edited my reply before I saw yours.
I checked and got these codes:
P0A80
P3000

I have a warranty, I'll get them out here to check or refund me.

 

Mendel,
I don't know, how could I check for this.
In the meantime I had an issue driving the car and here are the screenshots suggesting another bad battery:

 

I want to thank you all. I have read a common complaint about these threads is usually the poster does not have the courtesy to do a final update, just letting them die and leaving everyone wondering if there was a final resolution.
So this is what has happened.
The company told me that they thought that the inverter was possibly having problems causing the battery failures. They started looking at the whole charging system and found the 3 way valve was failing and leaking, the inverter pump was also failing pushing very little flow. I purchased a Toyota brand 3 way valve, the after market one failed in less than a year (code P1121). The company, for $625, replaced (they supplied) inverter, inverter water pump and another tested hybrid battery and installed the 3 way valve. They have given me a money back warranty if this does not solve the problem.
Immediately after the install my average MPG has gone up to 35.5 and still rising, numbers I have not seen in over 3 years. I hope this resolves the issue.