.35s are...different....
I grew up deer hunting with my father, relatives and friends in the Adirondacks of northern New York, in the early 1970s. We didn't often hunt the "southern zone" (designated by the game laws, it was shotgun slug only for deer there).
The rifles carried by our party members were fairly typical for the area, mostly Winchester or Marlins of varying vintages, mostly in .30-30 or .32 Special. Exceptions existed, Art carried a old Remington pump, (either model 14 or 141, I can no longer remember) that didn't have a shred of bluing left on it, anywhere. Caliber .30 Remington. Hiram carried a borrowed rifle, nearly always, although once in a while he had his own, until after deer season, when it would get sold. Often he used my uncle Jim's Savage 99 .300 Savage (Uncle Jim couldn't manage the woods any more).
My Dad carried a Winchester 94 .32 Special (because he got it virtually new and dirt cheap from a cousin's estate. Bob had a Winchester 64 rifle (.30-30). Uncle Lester carried a Marlin .30-30 for years, until he fell on it, and broke the stock off. The gun he replaced it with was another Marlin, but in .35 Remington. And I've seen others use the .35 too. For a long time, the only real reason the .35 Remington survived on the market was because of the Marlin rifle it came in.
The other Remington rounds in that family faded into the obscure/obsolete category. The .25, .30, & .32 Remington, by the 1970s were in that group that if you had one, and found some store that still had ammo, you bought it all, even if that meant you had to short something else for a while. Because there was no way to know when, if ever you would find ammo for it again.
(at 15, I was a beginning handloader, the only one in the group). Well, back to the .35...
It is my experience that the .35 Remington (and the other .35s too) have an effect on game that is not well reflected in the ballistics on paper.
On paper, the .35 Rem is not tremendously better than the .30-30. My personal experience is that deer do not know this. A good hit with everything knocks them down. A good hit with a .35 (or bigger) knocks them
over! I won't try to explain exactly why this happens, but I've seen it happen, more than once.
Between the .30-30 and the .35 Rem, the difference in energy and bullet size doesn't seem that much on paper, but the difference in the way the deer react (that I have personally seen) has been considerable.
Your experience might be just the opposite, but mine tells me that if the choice is a .30-30 or a .35 for deep woods deer, take the .35!
and just FYI, what I carried back then (and sometimes still do) was a Remington 600 in .308 Win.
It worked just fine, too!