While I'm a huge fan of adhesives designed in properly, from what I'm seeing is this is not a question of bolt size but more of mechanical advantage and how it can work against you. 5/16in or 3/8in vs. 1/4in is going to buy you little in the way of battling the prying load. See photo with load and reaction vectors. While they should be pointed in/out of the plane of the photo, you can see there is only about an half inch length (effective) couple to react the applied force at the top of the handle that is 25in length. This is a 50 to 1 magnifier. So you push 20lbs on the handle and you are developing 1000lb force on the bolt and flange not to mention the lack of stiffness when leaning on it."
Exaggeration. Unless you fall against it you are not going to push sideways with 20lbs of force on the upper most tip of the chain saw. Secondly, the practical aspects of the whole thing will show up only when you try it. Have you run this thing around some, temporarily glued on ? Think pitch, roll and yaw. My guess is that vibratory shaking around in the roll axis will be the primary problem (if there is a problem at all) in simply bolting the commercial saw holder onto the handy flat metal plate you are using for the attach point. Heck, bolt it on and go try it. If roll axis stability is an issue (due to your lunging sideways against the saw or due to tractor shaking and vibration) then devise a brace or added stabilizer that goes on down and mounts to the frame. There is some degree of inherent roll axis instability in the design of the commercial saw mount hardware -- you cannot overcome that without starting over and designing your own, maybe like a gun scabbard? Looks to me like you are within a few minutes' work of being able to go try it (bolted on of course.)