Paul,
I use a 12x50 Trinovid BN a good bit for birding and sightseeing. The detail revealed is staggering. I think enjoying 12x has more to do with accustomization and tolerance than being super strong and steady, which I certainly am not. The high weight, excellent ergonomics, and super wide field combine to make this particular 12x relatively user friendly and great fun for me. Also, the long straight roof shape makes for instinctive pointing. It really isn't much harder than 10x, and the rewards are significant.
But, I will not minimize the downsides.
Depth of field is practically nonexistent. A surprisingly distant tree will not be all in focus at once, and will require "focusing through". Even half a mile is not "infinity", you have to refocus to a mile. At a mile, you're about there.
12x is a bad deal if you are hiking strenuously with heart beating hard and winded. Here, you will see that motion blur looks a lot like the blur of bad optics, and will be frustrated.
It is a slow binocular. Heavy and slow to bring up, and slow to get to sharpest focus. Up close flitty birds are obviously a disaster.
Regarding the Trinovid per se, glass and precision, and view comfort too, could hardly be beat, but the older coatings relegate the brightness, contrast and color presentation to what, nowadays, must be called second rate. The 11 foot close focus is impressive for such a high power. Mine is a somewhat rare example, in my experience, of a perfectly smooth focus action. That really helps battle the narrow depth of field. It is undeniably massive at 40 oz. I use a bandolier style strap, many would recommend a harness, but a neck strap is not going to do it.
I also use a 10x50 Ultravid (non HD) as my main birding binocular. It lacks the long range detail ability of the 12x, but exceeds 8x, and is an altogether pretty good compromise. The wide field and lighter weight makes it just tolerable for close up warblers and such. OK, I still miss more than with my 8x. And naturally, its not as good as 12x on ducks way across the lake. Of course its later coatings raise its contrast over the Trinovid, but it is outside your stated price range.
The jump from 8x to 10x is significant, but to 12x is breathtaking. There aren't many 12x fans here but I am not alone. Still, the smallness of our number, and the common admonition "10x max" cannot be ignored. Am I just weird or what?
Still I'd recommend the 12x50, as it is such a refreshing jump from 8x, at least for me. 12x is a challenge that I enjoy. I'm not saying the Trinovid has got to be the one. The SE is undoubtedly contrast per dollar and also lighter weight, if you're more into that than the Leica's better design features. If you use binoculars a lot (even obsessively like me) you have probably developed skills that would make 12x fun and easier than you expect. Of course it will be a shock at first and you will think you can't manage it. But after a couple of days, you'll probably get the hang of it and feel the power of, uh, power.
Ron