^ This. Also, you absolutely need to check out the SmallRig Full Cage for Sony FX30 / FX3 4183 because it is a total lifesaver for doc work! I remember being out on a shoot in the middle of a windy pier and my old generic cage started wobbling like crazy... basically almost dropped my whole rig. It was terrifying! Ever since then, I only trust stuff with multiple points of contact. That specific SmallRig cage uses a side lock and the bottom screw so it wont twist at all, which is huge for safety. For your record button issue, this one is basically perfect because it has that huge cutout on top. Plus, the top plate is removable if you use the Sony XLR handle, which is amazing for keeping things low profile! For the a6700, the SmallRig Full Cage for Sony A6700 4336 is the way to go, seriously. I love it! They finally fixed that annoying screen clearance issue by making the side arm thinner near the hinge. You can flip that screen out all the way without it hitting the metal, which is fantastic for those weird low-angle shots. Tbh, Tilta makes beautiful gear too, but SmallRig is just so reliable for port access. I have had zero issues getting my bulky HDMI cables in there. Just make sure you tighten those tiny M2.5 security screws on the side... seriously, dont skip those or your camera gonna rattle around!

Ive wasted so much money on generic cages that ended up in my junk drawer because of those exact issues... record buttons getting stuck is the absolute worst. Last spring I was filming a series in a crowded market and my screen kept catching on a sharp edge of a cheap cage. I eventually switched to the Tilta Full Camera Cage for Sony FX30 FX3 V2 Black and never looked back. It is specifically shaped so you can actually reach the top buttons without gymnastics and it fits the XLR handle perfectly. For the a6700 specifically, here is what I would grab to stay under budget:

• Tilta Full Camera Cage for Sony a6700 Black
• The fit is way tighter than generic brands and the screen clears every time. It feels like part of the camera.
• SmallRig Half Cage for Sony a6700 4337
• If you just need mounting points on the left, this keeps the right side of the camera completely naked so there is zero chance of port blocking or button interference. Tilta definitely feels more premium and less like a Lego set than SmallRig sometimes. Honestly, just get the Tilta for the FX30 and you wont regret it.

I think the modular designs with side cutouts work well for screen clearance. Not completely sure about the record button tho, but I recall someone being quite satisfied with the half-cage setups.