Answering your question with questions of my own:
1. How long have you been playing?
2. Are you sure your horn is in 100% playing order?
3. 90's metal Link... what size tip opening, and what make of reed + strength?
I've played on a couple different horns and mouthpieces. I feel like maybe I end up with a similar sound after I get used to something new. But some things are always easier with certain gear. The link is the best altissimo piece I've tried.
The vast majority of tone work is done by a strong, supported air stream and a relaxed (yet firm) embouchure. Remember, sound is produced by the reed vibrating a column of air that resonates inside the saxophone's cone... you want the reed to vibrate as freely as possible to get that fat tone you covet.
I've been playing about 16 years.
I keep the horn in good order.
The link is a 7* and I'm using a #3 rico royal reed. I find harder reeds give a thicker sound but then they are too hard.
Can you get a tutor?
There is nothing like a person right there to get a solid basis for improvement.
Yeah, there's a teacher I could go see. I took a lesson last year when I was trying to get better at overtones, altissimo, etc. I could go back. I just thought I'd see what people here would say. I took lessons throughout middle school/high school too but that was a while ago now.
I like your suggestions in the first post.
I don't think there are any real problems with my tone at the moment, I just always feel like I'd like to sound a bit fatter.
Here's a random jam from a few months ago. I think I was playing the SML gold medal with the link. The Yamaha '62 is a little fuller I think, at least with the current setup. The SML had the thicker sound when I was playing the Eric Falcon Warburton LA with too hard a reed.
https://drive.google.com/file/d/1FG4X2iezs4RfEMe2K2yOdq5F3IOnIsnk/view?usp=sharing