The L4400 will move round bales with the loader, but only if they're dry and even then you wouldn't want to be driving up, down, and across too many hills. The 3400 is out as far as moving rounds. I know, as I once owned a 3400. Sold it because it was too tippy and simply couldn't lift enough.
I think the 4400 is the bare minimum to consider for this task. You could go smaller if you bought a spear for your 3pt hitch and moved 'em like that. If you're going to be moving a lot of round bales, and want to stick with a lower-horse tractor, you should maybe consider one of the heavier brands (Kioti, Mahindra). I say this having owned neither.
My father-in-law owns a 30HP Montana (not sure of the model), and I've moved fresh 5x5 round bales with that and haven't felt too unstable. The Montana feels considerably wider and more substantial than the 30Hp L2800 though. If you drop the loader two quickly you can pop the rear tires up a bit. Moving bales over a distance isn't bad if I just lower the loader quite low. His neighbor owns a New Holland TC35 and that seems to do really well with the bales.
I haven't compared the size specs of the Montana and TC35 to the L4400, but based on my own impressions, the L4400 seems more similar in size to the TC35.
Based on these experiences and what I was told about the L3400 (your input included), I think the 45Hp L4400 should work out okay for me with the round bales. I'll be moving maybe 60-70 bales a year, max off of a trailer and into a storage shed, then later into the pastures one at a time. So it's not an activity that will be done on a continual basis.
I'm still having a tough time wrapping my head around laying out the extra cash for a brand new tractor, but I'm also having a tough time passing up a 0%, 5yr interest deal. That's why I'm wondering if the prices I was given sound like they're worth it.