I wouldn't have a 410 Classic or S510 for field work. Little to do with balance, they are simply too long for my liking when hunting, especially when fitted with a silencer. Your question regarding balance with a scope fitted is impossible to answer without knowing the scope concerned. My own S410 has quite a different balance with the current 3-9x40 scope fitted than it did with a 6-24x42 that it used to wear.
I'd also rather feel a rifle have a fairly neutral balance but over the years I've found that I actually shoot better (particularly standing or kneeling) with a decent amount of weight forward. That's why my S410 carbine, used exclusively for hunting, has a Harris bipod almost permanently attached.
The differences between S510 and S410 are little more than cosmetic. The sidelever mechanism still actuates parts that are common to both rifles. The actual actions being the same. The other difference being that the 510 has a barrel shroud. Now this will act as a moderator to some extent but, for hunting at least, there's a good chance that you'll want an additional silencer.
I wouldn't pay the difference to get a 510 over a 410 in sub 12 ft.lb guise. I may well choose the sidelever if I were running an FAC variant on the S4*0 or 510 theme. However, chances are that I'd not choose any S4/510 as an FAC rifle anyway!