Don't do this.
The FR-2LE had a better headphone amp. than the FR-2.
Was the FR-2 even worse? Amazing!
But the headphone amp is like this for a reason - it's all down to current draw and battery life. A better amp. would draw more from the battery and shorten the recording time and the recorder is a field recorder, so the longer running time the better.
Of course it would increase power consumption, that's a given
I won't do it because I got a SD MixPre 3. It drains power like there's no tomorrow
but everything is amazing.
I will sell the FR-2LE including a new Tamiya compatible battery and charger.
The best headphones to use with the FR-2 and FR-2LE are the Sennheiserr HD 25 which are very efficient and give a good output at lower gain levels than other headphones.
I was using Ultrasone HFI-650 which are quite efficient. I also tried the Sony MDR-7506 lately and I think these are more efficient than the Ultrasones.
I asked this question to Fostex in detail when the first FR-2 came out and I wrote the first review of it for LineUP magazine and they told me the reason at the time.
I know Fostex are far from idiots and there was a reason. I haven't opened it but I imagine they used the codec-and-all chip.
Nowadays there are better components
Anyway I won't do it finally, better to sell it.