Based on what you've mentioned, A .444Marlin Marlin levergun might suit your ticket...I know it's not a pump, but you mentioned an interest in leverguns, the .444's got more stank than the .30-30, makes for a LOT better deer rifle in my opinion, but it's a lot more shootable than the .30-06...I'd also suggest a .44mag in the Marlin 1894, I get basically the same performance in the field as a .30-30 (a little more aching trajectory, but they're both good to 150-200yrds on deer if you do your part), BUT, the .44mag uses about 1/3 the powder, or costs half as much if you're buying factory loads (I've bought Winchester Super-X .44mag 240grn half jacketed soft points for $11 a 50brick, when $11 a 20box is a decent price on similar quality .30-30rnds=better than half the price for .44mag). I suggested the .444 because you seem like you're looking for more power than the .30-30, as opposed to equal power from a different round.

The .45-70 Marlin 1895Guide gun might also fit the bill, it's light and handy, and the .45-70 is an awesome hunting round, IT IS MY OPINION that it's more shootable than the .30-06, it's kind of like the .454Cassul vs. the .480R, the .480 and the .45-70 may actually kick a little harder by the numbers, but it's more of a shove than a kick, the .30-06 or .454C are lighter recoiling but kick like hell...So basically the .30-06 feels like a pretty hard kick to the shoulder, while the .45-70 feels like a really hard shove, it might just be me, but I've ALWAYS found the .45-70 to be MUCH more shootable.

I'm also not certain, but it seems like when I actually figured the recoil energy of factory ammo in the .45-70 Guide gun, the recoil energy was considerably less than that of typical .30-06 loads (in a Ruger MKII M77 standard).