What are the best gimbal stabilizers for Sony Alpha cameras?

Hey everyone! I finally pulled the trigger on a Sony A7 IV recently, and while I’m absolutely head over heels for the image quality and that legendary autofocus, I’m running into a bit of a snag with my video work. I’ve been trying to do more handheld 'run-and-gun' style cinematic shots for travel vlogs and the occasional real estate walkthrough, but even with the built-in Active Stabilization, my footage still feels a bit too 'jittery' for my liking.

I’m currently rocking the 24-70mm f/2.8 GM II lens, which is a bit of a chunkier piece of glass. I’ve realized that if I want those butter-smooth pans and tracking shots, a dedicated gimbal is pretty much a necessity. However, the market is absolutely flooded right now and I’m feeling a little overwhelmed by the choices. I’ve been looking closely at the DJI RS 3 series and some of the newer Zhiyun Crane models, but I’m worried about a few specific things.

First, I really want something that integrates well with the Sony ecosystem—ideally something that supports Bluetooth shutter control so I don't have to constantly mess with annoying cables just to hit record. Second, since I travel quite a bit, weight is a huge factor. I don’t want a rig that’s so heavy I end up leaving it in the car because my arms are giving out after twenty minutes. But at the same time, it needs to have a high enough payload capacity to handle my setup without the motors screaming or vibrating.

I’ve seen some people swear by the RS 3 Mini for its portability, while others say the standard RS 3 or even the Pro is the only way to go for the larger G-Master lenses. My budget is somewhere in the $400 to $600 range, though I’m willing to save up a bit more if it’s a 'buy once, cry once' situation that will last me for years.

For those of you shooting on Sony Alpha bodies, what has your experience been like? Is there a specific gimbal you’ve found that offers the best balance of weight, ease of balancing, and reliable performance with Sony’s menus and controls?