Re: Raking my brain on this F-class shooting thing....
You shouldn't have any worries about your rig at all. It should be fine to get started in an F-Class match, leaving <span style="font-style: italic">you</span> as the limiting factor. IMO, that's exactly where you want to be.
As you mentioned you can only practice out to 300 yd, it will be very important for you to get the best muzzle velocity data you possibly can, along with your actual drops at multiple distances out to as far out as your range allows. It's a little more difficult to match MV and drop data at such short range because the drops are quite small (a click or two to one side or another is very difficult to determine precisely at short range). However, you can use this data input at JBM ballistics online to get predicted drops from 600 to 1000 yd, depending on what range(s) the F-Class event(s) you're interested in shooting are. At the same time, you can generate windage data (also with the JBM ballistic calculator). If you have good data for your drop and windage at a specific range, your chances of being on paper with your sighting shots will be greatly increased. If you're not on the target to start, it's that much more difficult to get dialed in, particularly if the match has a limited number of sighting shots.
Bottom line is that to get feedback from the target puller (scoring/shot markers), you have to be on the target. Once on, dialing in will depend primarily on the wind conditions. From your description and accuracy numbers above, your rig is plenty good. Your ability to read the wind conditions is what will make the difference in your final score. Use the wind flags, trees, etc., and look into learning how to use mirage as a wind reading tool.
If you take these simple measures before your first comp, you should do fine. You'll learn a lot the first time about what you might want/need/do differently the next time. Just get out there and do it, and have fun while you're at it. It's really a blast and you'll meet some good folks along the way. Best of luck to you.