Are Gretsches Incurably Bright/Twangy?

I don’t mean the title to be a negative. They certainly have that reputation, but even if they have a predisposition to be bright and/or twangy, does that also mean you can’t warm them up if you were after say more warm jazz tones?

I have a G5622T, and I’m in my first year of playing playing the guitar so I may easily just be missing something here. My interests are in jazz and blues, but right now, I’m really just working on cords, cord changes and tone. I’m feeling like my B and E strings are incessantly twangy. It’s not a fret buzz thing, it’s the tone. I’ve turned tone all the way down. I have my amp (a Fender Champ II 25) gain, treble and bass around 5. I’ve played on the neck pick-up. I’m working on my pick attack to keep from hitting my strings flat. All of these things help, but it still feels like I’m really twangy. I do have flat wounds on it, which I like, but these two strings are plain steel.

I’ve heard some people say that Gretsches are just incurably bright. I’ve also heard people do sound comparisons such that you can’t tell the difference between guitars. Jens Larson is a good example of doing this. It seems like there should be a lot of tonal adjustments that could tune this out. I’ve heard others say it’s just the wrong guitar and to look at other 335 type guitars or PRSs, but the strings will still essentially be the same. Would a different guitar be really that different?