I may have over-emphasized the OAL issue. There is plenty of room to seat the bullets out to a "normal" range, but you don't have much latitude there. In mine, it seemed that it tended to tie up if I seated the bullets just deep enough to function through the magazine, but if I seated them a little deeper it functioned fine. I'm sorry I can't be more specific with this, but it has been a few years since I loaded for it. I had a fellow, C.P. Donally(?sp), a gunsmith in Grants Pass, Oregon, look it over for me (I have lost track of him and do not know if he is still around, but he impressed me as an authority on 9.3 caliber.) He said that adjusting the feeding rails was a case of "chasing your tail", so he did not modify them. That is the only modification I think you might consider, but make sure that whoever does the work is an expert, because you obviously cannot back up and start over - at least with that action.
I can not advise you about the throating, since mine was "standard", as far as I know. I don't think there needs to be anything special done with it, however.
As far as case rim and head dementions - the 6.5x55 and 9.3x62 are "basically" the same. I say "basically" because I think there is some conflicting information about this, if you look far enough. The last reference I looked at shows the 6.5 with a rim diameter of .480 and head diameter .480, while the 9.3 shows a rim diameter of .470 and a head diameter of .476 - compared to a 30-06 with .473 and .473 respectively. I don't currently have any 9.3x62 ammo around or I'd put a caliper on some. I do know that the bolt face of the 96 action seems to handle either the 6.5 or 9.3 equally well and I don't think there is any cause for concern there.
Building a 9.3x62 on a Mdl. 96 action is really very straight forward and can make a beautiful sporter. The 9.3x62 is probably a better cartridge than the 35 Whelen and many magnums (and I love my 35 Whelen!), but be prepared - lots of people are going to try and talk you out of doing it. They will tell you that the 96 action has this problem or that problem. Then they'll tell you that the 9.3x62 is an oddball, even though Europe and Africa have used it since around 1905. In truth, the 96 action is plenty strong and the cartridge itself is great, as long as you load it like the factory loads it - moderate pressure and velocity. Don't try to make it into a magnum, because that's not what it is. But, it will kill as though it was. It's modest velocity will allow that heavy bullet to mushroom and still shoot through most everything. I doubt you'll ever recover a bullet, unless you shoot lengthwise into something very big.
If you want to talk more, you can e-mail me at: carleb@rectec.net