Your problem is using LED bulbs combined with using an inverter. LED light bulbs' internal AC to DC converters are adequate but cheap, and do not tolerate anything unexpected very well. And what they expect is a 50Hz or 60Hz relatively clean sine wave at around their rated voltage.
Your inverter is almost certainly of the 'modified sine wave' variety. This type of inverter works by adjusting the output voltage in 4 large steps. This is, at best, vaguely reminiscent of a sine wave, but its really just a bunch of half-step square waves. For a lot of applications, or even most, this is fine.
Unfortunately, LED light bulbs do not react positively to this abuse. If they are given a modified sine wave like the output of your inverter is giving them, they will literally poop all manner of horrible harmonics directly into the eager mouth of your inverter. This will make the inverter hemorrhage watts in the form of waste heat, while making the bulbs also run hotter and there is even a risk that they will be damaged by these harmonics.
Your math is fine, just remember to add in an extra 200W of harmonic losses, and you get that magic 3-4 hour figure :).
The idea is sound except for this unfortunate 'gotchya'. Possible solutions:
Use a pure sinewave inverter. These are more expensive than modified sine wave inverters, but really not by all that much these days. If time is the most important factor and dropping another $100 or so is acceptable, this is probably your best bet. You can buy them at most retail stores that carry inverters. They may be a bit overpriced at these locations, but I like to think of it as the 'I need it NOW!' tax.
Use an isolation transformer between the output of your inverter and the LEDs. The transformer will 'sine-ify' the squarish output of the inverter and put your LED bulbs at ease. Not sure how easy it would be to find one in a hurry though.
There are other solutions but they all require buying things off mouser and waiting days, so I won't bother mentioning them. I think the best route would be to just get a pure sinewave inverter, one of good quality. Drop that in with your existing setup and you should get 8 hours no problem. Yes, there are conversion losses, but it should be, and this is absolute worst case (it ought to be much better than this), 20-30W tops in addition to the 43W load. Even at 75W, 80Ah is plenty for an 8 hour run time.