I was thinking no more than halfway, just enough to keep it secure. The holding cords are stretchy. I don’t intend to bring it outside in the rain currently anyways. Thanks Russ!
Do you have a sander? A belt sander would work great. Just hold the cap level with the bungee's, and sand it down a bit. Not much clearancing required by the looks of it. edit- Secure that scope like it should be. If the cover doesn't fit, so be it. It's there to keep dust out of the objective lens when you have it standing in a corner. Plastic wrap would work as well.
Mounting it low and tight over the bore is the best way....just like you have it. I have notched out the dust covers to fit exactly like what you are needing to do. They still fit fine and do their intended purpose with and inch or so cut out of the bottom for clearance.
I wish I could get to my Dremel tool. Unfortunately it’s not a super easy accessible item right now deep in a storage box but again cheap and actually good sight scope, I will modify. I feel better, my brethren. Most thankful of you all!
