[...]After the crash the steering felt off, less stable, but I figured it was because the forks were slightly misaligned. I just got the forks rebuilt and realigned last week, and although they're straight the feeling is still there. At slow speeds it just feels so much more easy to tip left and right. When I used to take corners I'd tip it in and it would just feel like it fell into a line nice and smoothly. It still falls into the turn but it doesn't hold the line the same. If I brake with any lean I can feel it trying to pull the handle bars towards the lean much more than I've felt before. And overall just feels like it's floating more, not getting the feedback I'm used to.[...]
To some extent this sounds like a good problem to have.. one way or another you seem to have more front grip, meaning you can turn-in later and get back on the gas earlier. It's a characteristic I'd been trying to tune into my 600RR for a while.. coming from a Ninja 300 that had fantastic steering response. For a while I ran with the HESD disconnected, but the minor improvement wasn't worth the head shake on hard corner exits. I also replaced the rear shock with a Penske and revalved the front end with GP Suspension's 20mm kit. And with some amount of fiddling it added up to a responsive and confidence-inspiring ride. The last thing I tweaked seemed to make the biggest difference---as these things go---and that was adjusting the geometry.. raising the rear end with the Penske's ride height/length adjuster, and lowering the front end by raising the tubes in the triples.
What's interesting, though.. I recently swapped my forks with a pair equipped with GP's 25mm cartridges, and they must have more minimum installed preload because the front end sits about 5 mm higher now. But here's the thing: between the stiffer damping and the improved mechanical grip this setup steers even faster.. in spite of "stabilizing" my geometry. I'm thinking now I may lower both ends of the bike closer to stock height.. that or I need to extend the kickstand.
Anyway, if your fork oil was worn out, a rebuild can and should noticeably improve your front grip. If it was behaving differently turning left vs turning right then I'd agree something is wrong. But otherwise it could just be a matter of adapting your riding technique.. i.e. turn in later, use more throttle earlier.
If you can't (or won't) compensate and get accustomed to the new feel/feedback, you do have some ability to adjust the geometry even with the stock setup. Decreasing preload on the rear and/or increasing preload on the front will let the rear squat further and make the bike steer more smoothly and feel more stable mid-corner. [Do you know what your sag/preload settings were before?] The damping adjusters can also affect dynamic geometry. If rebound is too slow/compression is too fast that end of the bike will suck down into the stroke as you roll down the road. Conversely, if compression is too slow/rebound is too fast it will dynamically jack up that end of the bike. An experienced suspension tuner (which I am not) could identify this by simply pushing on your bike and observing how it responds. I would suggest you reach out to the tuners in your area, e.g. Catalyst Reaction, Super Plush.
There are a couple things you can check on your own, though.. assuming you have the tools. Check your front and rear suspension adjusters to see if they match the stock settings in the manual. [And feel free to explore the full range of adjustment. You can't go dangerously wrong with the stock adjusters.] At slow speeds the HESD is designed to have little damping effect, but it couldn't hurt to check it. There's a test procedure, here: https://www.600rr.net/vb/35-maintenan...e-07-08-a.html
You do need to safely lift the front tire off the ground, though. A rear swingarm stand and a hydraulic jack under the headers works.