Does anyone here have experience with one of these "big bore" AR15s and a ballistically comparable 45-70 in a lever-action or bolt-action rifle?
No experience with a big bore AR-15, but lots of experience with ballistically comparable 45-70 lever guns, from 1873 Springfield loadings all the way to Ruger #1 loadings. Unless you're planning on having a 100yds between you and the bear and the bear stands stationary for the first 3 shots, forget any AR platform rifle & anything that can't replicate Ruger #1 45-70 loadings in a lever gun. The AR isn't able to handle the high case pressures associated with rounds capable of one-shot stopping a charging bear thats hell bent on killing you. A Marlin guide gun loaded with Garret or Buffalo Bore Magnums is the bare minimum for 45-70 as bear defense (they both have 430gr loadings @ roughly 2000fps and they generate enough muzzle energy to be legal for hunting everything but elephant & other similar sized game in most parts of Africa). Those are powerful loads that replicate the energy of medium bore magnums to low end large bore magnums. Another option would be a 1895 in 405 Win as its pretty close to what you'll get out of a hopped up 45-70.
If you're really set on a semi auto, it has to be a BAR. The Mark II BAR is strong enough to handle upto a 338 Win Mag, which nearly replicates the energies of the 375 H&H Mag.
My priorities (in order) are 1) all weather reliability, 2) shot placement, 3) ballistics, 4) felt recoil, 5) cost and aesthetics.
I'll match your list as follows:
1) Browning BAR Lightweight Stalker in 338 Win Mag or Winchester M70 Safari Express in 375 H&H Mag. They both have iron sights, but the M70 uses Express sights (we are talking a gun that is a life line and these are the only two guns I'd put my life on the line with if I had a bear charging me).
2) Shot placement depends on you as a shooter. Bear defense guns need to have the power to be able to do a one shot stop on a charging bear, which necessitates the use of medium to large bore magnum chamberings. So if you can't handle recoil well, look into recoil pads (both for your shoulder and the buttstock), muzzle brakes, and some gun work to free float your rifle barrel. All these will help reduce recoil.
3) The 338 Win Mag has a bit more range than the 375 H&H Mag, but both are plenty fine out to 300yds. Both cartridges have MPBR's (max point blank ranges) around 250yds, so they have the range for the quick aiming & shooting for charging bear defense.
4) Again, a rifle capable of stopping a charging bear with one shot needs to have a large powerful round to do so. This means you'll have to deal with large amounts of recoil, so you need to find what you're recoil limit is. Find a place or friend with various rifles in the required calibers and do some shooting. A rifle that has the ability to stop a charging bear is of no use to you if you can't shoot it. The BAR in 338 Win Mag will have less felt recoil than the M70 375 H&H because the BAR's action absorbs some of the energy and it comes from the factory with a muzzle brake.
5) Both rifles I listed go for around $1300-$1600, but they are as aesthetically pleasing as you can get for mass produced rifles.
The simplest & easiest plan is to avoid the bear in the first place.
