Marek313,
Regardless of your saying this is a "rant" of some sort in your OP, be sure to know that there are some of us who, even though we sometimes do not post a reply, actually enjoy reading about others doings & what might be offered for advice from others who are trying to help out, as well.
So, your "rant" is actually helpful to some folks, even if you did not realize it.
IMO, "Rant" all ya like,as it is just another way to get info shared when info is given about the "rant" & what others offer for assistance to alleviate the rant. ( "Making some lemon juice out of the lemons" you got.)
Anyway.... Her is another vote for using a shooting rest of some kind to find out what the firearm can do.
(Usually a "bench rest" or a "prone rest" setup is best. But, most folks likely already know that...Some might not.. )
I think it is best to use the most stable position & rest you can, to test accuracy and verify where the firearm is shooting with a "baseline" ammunition before you try to work on any changes & then do the changes, "one change at a time", without doing any other changes, to get the best most accurate results of what is happening .
( For me, when I say "stable", that is a table(bench) and sandbags for pistols. Although sometimes I use a "V-notched jig" made out of some 2x6 or 8" material with a leather strip in the V to protect the firearm when shooting and small sandbags to hold it steady. I have difficulty getting up & down due to health issues for any prone positions, so that is rarely done by me now a days, or I would likely use that position for both rifle & handgun. So, it has to be a table w/sandbags or shooting stick or sticks(bipod) for me.)
Some folks use a walking(shooting) stick with a wrist loop which is either twisted around their "off/support hand side" wrist, or looped around their thumb/palm/whatever suits, with the back of their hand up against the stick to help be stable & that should certainly be more stable than just offhand, as well as being easy to use at your range even if it is busy.
You could also consider a"bipod" setup since you are going to a range, but you would have to figure out the best "mechanics" for how to rest either your wrist or your firearm to be comfortable as well as stable.
Some or many may already know what I am posting, but I am trying to help out here in my own way & as far as I am concerned that is one of the best reasons for a forum like this.
Helping out others if/when ya can, the best ya can.
G'Luck with your experiments & tests! I hope you get your solutions & satisfaction from doing it, as well as please take the time to post up what you end up finding out for results & what issues get solved.