4001S..... find an old one... with a nice thin neck and some clank !
All kidding aside, yes, RICs are a different beast, and really are a lot more versatile than what a lot of folks give them credit for. You can have as much down low as you've got on top if you want to.
Setup can be finniky, but I have no plans to swap out to a hipshot. The classic look is part of the allure to me. I think the Hipshot bridge is far less attractive.
Double truss rods are a minor deviation and a non issue really.
The neck profile can be awkward for a lot of folks and be a real non starter for some. It takes some getting use to.
I'm down to 4 right now. All all modern 4003s of one variation or another. I've had a few others over the last couple of years and have to say that the neck profiles on those are the reason they've moved on.
Would I entertain the thought of a 4001S or a Standard in good condition?...you bet!. But you have to be careful on those older ones too. Some of the necks were weak right at the neck pu route. That, and how the truss rods have been managed over the years would be my biggest concern. I should never have sold my '76 Burgundyglo that I bought brand new.. It was fantastic..
So OP, yes, I would definitely explore getting a RIC. It's one of those itches that once you have it, MUST be scratched or it will drive you crazy.
...but keep the Precision too. You will appreciate it once you have your RIC.