Here is my take on the various LA-3A mods.
On my LA-3A, original in every respect, and serial number 4093 (anyone know the date on that?), I have found that this thing will put out an incredible 40VAC p-p into a 600 ohm load at clipping. That is a lot of signal in a digital "18dB of headroom" world.
At the 50dB (high gain) setting and the gain knob turned fully clockwise the maximum noise I measured was -79dB. In a typical setting on a vocal, and at the 50dB setting, I set the gain at "2", about 40db less gain than max.
The noise doesn't seem terribly offensive so far, mostly 1/f noise with a corner frequency of 125HZ.
Now, the mods.
The circuit mod as proposed by Ed Evans changes the main feedback resistor (R14, 220k) by adding a 15k resistor in parallel to it, making a total resistance of 14k. This reduces the gain by 12.4dB and makes the operation in a +4 world more manageable. It does this by increasing the negative feedback. Increasing the negative feedback in an amplifier raises a red flag for me. I wanted to know what this mod would do to the transient response and the balance of the harmonic content of the distortion in the circuit.
My initial findings are what you would expect, in the original configuration the distortion is largely 3rd harmonic and the higher harmonics increase smoothly as the signal level increases. This makes for a nice fat dynamic character. The modified circuit tends to increase the higher order distortion products more abruptly. This tends to sound more raspy. you certainly know when the circuit is clipping!
As an alternative to the Ed Evans mod, you might want to pad the output by making a voltage divider of three resistors connected in series across the transformer secondary , a 270 ohm - 100 ohm - 270 ohm. The output XLR connects across the 100 ohm in the center... This will allow the output transformer to saturate a bit too, if you like that sound.