In addition to miiind's great advice (and +1 for VSL). There's also EastWest who sometimes offer a free month of their Composer Cloud service, which has a few pianos as well. Though they don't continuously offer a free month of their service, but that's about it beyond what's already been mentioned that you can try free.
I remember that about 15 years ago, there was another cloud service that allowed you access to a virtual machine for something like 15 minutes that you could reserve to test a given library. I can't remember the name of the service and the likelihood that it's survived is tremendously unlikely, as such services can be absolutely fraught when it comes to ToS concerns.
You could also try local sound studios or even a nearby University, both for recommendations or even being able to freely or affordably try things out.
I know that most of the composers I know who want a woodier sound "render" out to an acoustic that's close-miked with a midi like a QRS or Disklavier system.
It's been a long time since I seriously shopped for a PTQ alternative, but I remember that Imperfect Samples had more "woody" vst options than most providers (but that's probably a decade-old opinion).
If I were in the market for more Piano VSTs, I'd probably either go for VSL's Fazioli (please PTQ...please add a Fazioli!) or just save up to get a rebuilt golden era grand and add QRS to it--but I so don't have anywhere to go with an acoustic of any real size in my studio. Once you get to the point that a "good" controller/keyboard is $3-6K USD plus another $500-1K USD for a good library set, you may as well consider an acoustic for $6-10K USD, as those price points start being more about business investment and future value. Spitfire also has decent pianos from what I've heard, but my experience outside of the PTQ market is too minimal to provide top-quality advice.
Spotify:
https://open.spotify.com/artist/2xHiPcCsm29R12HX4eXd4JPianoteq Studio & Organteq
Casio GP300 & Custom organ console