Hi,
What rifle do you have? I had a Rossi and it did not feed ammo well/reliably, and took it back to the dealer and got a Marlin 1894. I took the rifle apart and polished all the moving parts, which greatly improved feeding and general handling.
With the longer rifle barrel, avoid powders faster than 2400. Win 296/H110 works well and gives high velocities. I have not tried Power Pro 300 MP, which will give high velocities.
My rifle does not feed smoothly with 300gr bullets, but it does feed, and then shoots well. For hunting try the 240gr and 270gr Speer Gold Dot (bonded bullets), the 250gr Partition Gold or 240gr Hornady XTP or 265gr Hornady Interlock. If you want to hunt any animal larger than the deer, the 300gr bullets my give better results in the rifle, but you may have to shorten the cases or seat the bullets deeper to get them to function/feed in the rifle. Both the Speer and Hornady 300gr bullets have two crimping grooves in order to allow you to seat the bullets deeper to ensure better feeding through the rifles. Hornady lists loads only up to 1400ft/s, while Speer shows loads just over 1500ft/s.
Remember that if the 300gr bullets are seated deeper, the case capacity is reduced and the powder charges are reduced accordingly. Some reloading manuals actually show this in their rifle load data.
In my rifle I get about 250ft/s more with 240gr bullets and about 150ft/s with the 300gr bullets than from a handgun (I have chronograped 5 different handgun barrel lengths, from 4.2" to 10.5"), so the 44 Mag in a rifle becomes a very powerful cartridge for short range use.
I have only used 240gr lead SWC in my rifle, but avoid lead when possible, so cannot give much input. Others have found heavy 300-320gr bullets very effective, even if it means feeding the first cartridge directly into the chamber, and then having lighter bullets that will feed reliably from the tube magazine, loaded into the magazine.
Hope this helps.
RSA1