Does anyone have experience modding the lepai output section? toroids + Caps, etc...
Usually toroids are transformers in the PSU. A linear regulated PSU can be made very clean, and toroidal transformers are better (and I believe more efficient) and more expensive than other types.
Upgrading the PSU can produce noticeable changes in the sound, especially since the amp usually references the voltage rail and ground when outputting. That said, it's a non-trivial mod, and you'll need a new case for it.
Output capacitors are one of the "things" in audio. They're great for what they do in a design, and designing something without them is much more difficult. On the other hand, people do say they impact the sound, and there are some "better" (more expensive) ones you can use that might make a difference. You start to verge on subjective (snake oil) territory here.
If you are replacing capacitors, only get audiophile grade ones for capacitors in the signal path. Other capacitors can be replaced with high reliability ones, or low ESR organic types (If the amp doesn't have them already). The way I do it is mainly just worry about electrolytics. ceramic/tantalum ones are usually good, though they can get microphonic in some cases.
As far as the "output stage" of the amp. the amp usually has a voltage gain stage followed by a current gain stage (or buffer). Upgrading the current gain stage can give you more power, etc. Usually current gain stages (buffers) are very very transparent (for a number of reasons), and can range from being simple (a single transistor) to very (very) complex.
Note that I haven't seen internal pictures of any T-amps, and most of my knowledge is for headphone amps (not speaker, guitar, or mic amps) so take what I've said with a grain of salt.