The ESP Guitar Company

Intonation is making sure that your guitar stays in tune for each note on the fretboard. It depends on the length of the string and it adjusted at the bridge. You test intonation by making sure an open string and its 12th fret tone are EXACTLY the same. If not, then your intonation is off and your guitar will play out of tune all over the neck.

Second, intonation PROBABLY would not affect dullness or shittyness versus just being out of tune. Does it stay in tune (aka is the tuning knob faulty)? It could just be that because you used a smaller string gauge, it doesn't sound that great 2 steps down. Try tuning up to E standard and check the tone there.

if the sound on a plain string is really dull sounding that means that there isn't enough tension on that string for it to resonate properly, given the material of the nut, if you tune that string up back up to a G and listen to it, that would be your sign that it there is not enough tension. you can replace your nut (in a drastic case), but you could try getting a gage of strings that are tight enough but still give you nice tension on the plain strings

11-54's should work, i use these on my strat in this tuning and its known for having a bad g sting (sounding dull and shitty) but with that gage i dont have any problems.

if you still do have problems installing a string retainer and getting a more dense material nut will help. the retainer will hold more tension over the nut and a denser nut material will allow the string to resonate properly.

i like a really high tenison, so i normally use 12-56 or 13-60
first time i used a plain string tho.