I have 2 suggestions for you. I have been playing for 25 years. Growing up, Steve Harris was my idol. Today, I am a huge Tool fan, I freaking love Machine Head, and I'm into pretty much anything Max Cavalera does. So, I listen to the heavier end of the spectrum.
I have 2 Fender Precision Elite IIs. They're the best basses I've ever played or heard. Very, very rich, full, deep tones. They weigh about 13 lbs each - about 6 kg. So, they're a little heavy. As I've bought heavier basses, I think the sound quality has increased immensely. Wood density matters. They've got two sets of Fender split lace sensor pickups, (the II has 2, the I has 1) one in the middle and one near the bridge. The bridge is a fine-tuning bridge, about the same mass as a Badass. They also have a 3 way preamp switch that can be turned on for one pickup, the other, or both. The same type of switch is for the tone control. You can get ANY sound out of these basses, especially if you have a good amp. I play through a GK 1001-RBII pushing an SWR Workingman's Tower (8x10). When I crank my rig, stuff falls from the ceiling. No exaggeration! Right now, I have the eq set to sound somewhere between mid 80s Steve Harris and Justin Chancellor. It sounds freaking phoenominal!
I used to have an '80 Precision Special. I wish I still did. It was the forerunner to the Elite series. It's essentially a P Elite I. It has a single split pickup and a preamp. Very similar sound. I don't think it was quite as heavy as my Elite II. I guess I'm partial to active electronics. 5 of my 6 basses are active. My only passive bass is my Fender HM, which has 3 Fender jazz lace sensor pickups. I really like Fender's lace sensor pickups.
If you save a little bit more money, you should have enough for an Elite II in very good condition. But, they're not easy to find. Many of the ones I've found for sale are beat up. While some of the nicer ones are immaculate and simply overpriced. Most people that have them love them as much as I do and don't want to let go of them. I've seen pictures of guys' collections that have 7 or 8 of them. I would like to collect them. Everywhere I go, people see it and say "Wow! What is that bass? I've never even heard of these, much less as seen one. THAT is awesome! Where can I get one?"
So, those are my 2 suggestions. 1) a P Elite II 2) an early 80s P Special. Brother, either one of those will put that Thunderbird to shame. No offense. But they're not even in the same league. Of course those are just my opinions. And remember, opinions are like buttholes. Everyone's got one, and everyone
else's stinks.

Hope my input helps a little bit. Best of luck in your search! Jam on!
