If you are left eye dominant and right handed you will find it is easier to learn how to shoot left handed.
I disagree. If you shoot like you are you will never be a competitive shooter. It just wont work with rifles. It will work with shotguns and some odd looking extra equipment though.
I don't have the time, money or space to shoot everyday, but I shoot once every week.
Shooting once a week is a lot. It may not seem like it on this forum, but on this forum the regulars are pretty much all in the top 1% of shooters as far as money/time put into the sport(not saying skill). Or they are totally full of crap. I have shot rifles, pistols, and shotguns in amateur competitions and I am on the extreme low end of the regulars here. Either way, I wouldn't use what you see here as a judge of normal shooter behavior or how much you need to be shooting to be good. Once a week is plenty. If you dry fire another day a week for 20 minutes you will be in very good shape. As much as you are shooting my guess is that within one month you will have decided learning to shoot lefty was a good idea and you will be shooting much much better with in two. In six months you will be able to show up to local competitions and at least not be in last place, probably do decent. Assuming you practice correctly.
If you won't heed the advice, then an eyepatch/obscured lense is the solution. The offset systems have come up before and other places and they do not work well for rifles like they do for shotguns. THink about how much target shooters put into getting the scope low to the bore. Now think about moving it 4 inches to the left.
"Eyebrow, yes, but i get too close to the scope so it whacks me most shots. unpleasant, but not painful unless I do it a couple hundred times"
I highly recommend you not allow this to happen. Use to set up the scope correctly or buy a decent scope with enough relief. There are very cheap scopes for the 556 that will work fine($50). It may not be painful, but i seriously doubt you can do this without it effecting your shot(flinching). Your mind can't know something will be coming back and hitting around your eye without it trying to pre-empt the contact. Claim what you want, but I won;t believe it.
If the AR platform interests you, the AR15 in 300Blackout might be a good compromise.
I agree, except that it won't be a compromise. I don't have one, but for what almost all civilians are using their ARS for the 300 blackout really performs a lot better than 223. With "everyone" owning an AR now I expect to seem them used a lot more for hunting and for how most of us hunt the 300 is great and it will get cheaper if it grows causing more growth.
I would only get an AR if you either want to make a real target rifle out of it OR you want to buy multiple uppers for it. Keep in mind that if you buy uppers for different things the lower will not be specialized for them. For instance if you have one 223 upper for competition shooting it will have a target trigger and if you have one 300 blackout for hunting and home defense that taget trigger will not be the best option, so most end up getting multiple lowers also and don't utilize the modularity all that much(the lower is cheap compared to the upper, accessories and optics).
I have not seen anyone, including people who compete with ARs at Camp Perry with an AR set-up I really liked as far as cheek weld. Most say it is very important for accurate shooting. I shot my AR better than my Garand because of the low recoil, but I hated the cheek weld on it and it negatively affected my shooting.
You don't walk to around in the hunting woods with an AK ... trust me!
To be frank there will be some people who will not invite you back hunting if you show up with an AK. Less so with an AR that is set-up for hunting. Maybe you won't want to hunt with them anyways, but most of us are desperate for land access. I had a land owner tell me they MIGHT let me hunt coyote on their land if I use my muzzle loader. I will probably go for it if they come back saying yes.
My suggestion:
Get a 03 FFL(C&R), then buy an SKS and a few bolt guns in various cartridges. You can get some cheap sporting stock for SKSs that make them a lot less tactical. Play around with them a bit, find out which you like and get it set-up for your needs. At least they will all come with decent sights.
Alternatives I do not know much about that come to mind:
1. the 5.7 as other stated, but I think ammo is expensive and same problems as the 223 for hunting at range and legal limitation
2. the 7.62X25- Some semi-auto carbines available for it. There have been some bolt guns at different times available on the used market. Still the cheapest centerfire out there I think. Ballistics not too far off from 22 mag or 5.7. The cheap surplus is corrosive.