olo, I think you misread the graph in the coppertop DS. The 1W discharge curve hits 0.9V at around 16 minutes.
The TPS61029-Q1 DS doesn't have perfect graphs for seeing what it would do in this situation, but my interpretation is that it would start out with an efficiency in the low to mid 80's, drop rapidly to 80%, and end up down at 70% (that point is on the graph), at which point you'd be pulling 621 mW from the cell to get 435 to the LED. I would estimate that you should theoretically be able to get your 435 mW for a good part of an hour, say 45-50 minutes, but definitely not for an hour.
For comparison, the QX5252 DS has no mention of efficiency except to say "maximum drive efficiency can exceed 84%". Likely in this application it would be lower than the TPS, but that's not certain. I would say it's very unlikely to be better than the TPS part overall, and probably worse.
I checked out what NiMH should do. Discounting the BatteryGuy brand that claims 1800 mA-H, and PKCELL, with whom I am not familiar, the highest rated capacity was a cell from FDK (division of Fujitsu) at 930 mA-H. It's DS shows average discharge voltage (at 1A) is very close to the coppertop (at 500 mA) at around 1.2V. But the 1000 mA curve hits 1.0V (compared to 0.9 for coppertop) at 900 mA-H, or 1080 mW-H. That's double the coppertop's performance.
Unfortunately, it's really hard to acheive the datasheet specs when working within the constraints of a tiny flashlight, especially if the budget is low. The fact that it's bleeding edge tech combines with that to hamper you from obtaining the performance you find theoretically possible. Still, it looks like Linx Arc is correct that you should be able to get 100 lm for >1 hour from a NiMH AAA cell. It would only take >50% efficiency in the driver. That should be achievable with either of the chips mentioned in this thread. And if 1800 mA-H cells ever become real, WOW!
And FYI, we will NEVER see 350 lm/W on ANY device creating white light. The exact number depends on the color temp and other spectral characteristics, but it's generally agreed that the maximum possible for white light is around 270 lm/W. This is because 270 lm of any light that we would consider white (with no ultraviolet or infrared) contains around 1W of radiant power. Thus it would take 100% radiometric efficiency to reach 270 lm/W. It is physically impossible to exceed that no matter the technology.
It's true that you can exceed 270 lm/W, but only by adding extra green and/or nearby colors. Then it's no longer what most of us would accept as 'white'.