Does anyone have a preference between these two powders for 180gr roundnose bullets? Looks like 4350 may have better loading density. What about with 220gr roundnose bullets?

With the heavier 220 gr RN, IMR-4350 is your best bet.  40.0 grains under that 220 gr is about as close as you can get to the original .30 Army round.

As for the lighter bullets like the 180 gr, you might consider a slightly faster burn rate like IMR-4064 or 4895.  IMR 3031 is faster still, and although you could work up loads, I think it would be better suited for much lighter bullets like 150 gr and lighter.

3031 was a pretty good match for 30/30 130 grain flat points. I chose a load half way between minimum and maximum and was happy with the velocity and recoil. The flat tip bullets expanded pretty good at the higher 30/40 velocity. It would have been good for southern white tail and coyotes. A little light for pigs, some of them ran a pretty fair distance.
For 180 grain and up go with the forum wisdom and experience.

Funny my dad went  with  100 gr plinkers with 20 grains of Unique in 30.06. South Texas white tails are not that big!

Actually South Texas white tails had a reputation for being larger than hill country white tails. The state game biologists have made so many counter productive rules we are now having an over population of inferior deer. Every one in the local volunteer fire dept has quit hunting deer also, too many rules. I saw 20 deer in the 200 yards from the house to the shop, no big ones.
The only ones that get to really manage the deer herds are those with high fenced places that can hire private biologist to give them the go ahead to thin and cull. If you ask me the state biologist are making work for them selves, so they can manage private herds while wrecking everyone else's hunting.
Do not ask me how I really feel!

"Load density doesn't have a significant effect on accuracy in an iron-sighted battle rifle."

So far in my jacketed bullet experiments, it appears to me that I get better accuracy with powders that give full pressure at slightly less than 40 grs.  Like the max 3031 load with the 180gr bullet that parashooter has posted.  That's been with bullets ranging in weight from 123gr up to 168gr.  Could be a lot of different factors, it's just something I've noted.