I have seen the Baikal sxs in 30.06. I also found it nearly impossible to get my head down far enough on to stock aligh the sites. They are quite light for a 06 but they are quite manageable.

I have shot the over/under in 30.06 and 308 and they are quite good to shoot with regulation being no problem. The 308 appears to regulate best with 150 grain bullets and the 30.06 regulates with 165 grains. The extractors have a projection that fits into the extractor groove to pull the case out far enough to grab with the fingers. They are not quick to reload. One way of solving this problem that I have seen and it works very well is in the 308, have a recess cut for a rim and use the 307 winchester case resized in the 308 dies. For the 30.06, use 7.65 mm rimmed case,trimmed back to 63 mm, and resize in the 30.06 dies open the neck up to 308 dia. In 308, after firing, opening the gun and tip it up, the cases just fall out. I have not seen a 30.06 modification but I am aware of two that have been successfully done and used.
Another modification is taking a single trigger from a Baikal over/under shotgun and fitting it into the rifle. I have used a side a sxs 30.06 with this modification and it works well once the trigger has been worked to give a reasonable pull.

One over/under in 30.06 that I have used had the double triggers worked from 11 1/4 pounds down to 5 1/2 pounds and very crisp.

I am waiting for my Baikal Over/under in 9.3x74 which is supposed to be in by the 4th February. I am assured that there are several on there way.

I hope this helps.