"but despite this relationship AR owners and AK owners do not like each other"
Actually theres no problem between AR and AK owners, whats to keep us from liking each other, we just prefer our own choice of rifle over the others rifle. The only AK owners that most AR/M-16 owners or users dont like are those who are shooting at our soldiers with them.
As for the mini-14, even with improvements in the new models they are inaccurate compared to the AR. Why else would Ruger decide to make ARs, its a niche they had no rifle to fill.
There are many gas piston ARs now available, due to prices Im sure there is little to no wait time on most of them.
There are many rifles available that are similar, in fact the sig 556 is similar, uses AR mags, but is not an AR at all in any way, again pricey.
Some of the other choices such as the SKS, or garand are rifles from other niches altogether, none fit the description of either an AK or AR. The FAL is comparable to the garand or M1A, different type of weapon.
Decide which you like, and want, or buy a few different models.