+1 on what bugs said
You'll be giving up a lot of ground (speed) using a 300g bullet in a 4" bbl.
I'd go with a 245/250g cast bullet, you can get these to run in the 1200fps range out of your 4" bbl's along with being able to load them mild for play/practice.
A 250g bullet going 1200fps will penetrate a lot deeper & create a larger wound channel than a 1000fps 300g bullet. Both bullets have enough mass to get the job done. I'd rather have 20% more penetration on a bear myself.
If I was using a longer bbl (7 1/2, 8 3/8, 10, 14, ect), the 300g bullets would be an option.
Some thing else to think about: JD Jones came out with the heavy 300g bullet for the 44mag years ago to aid in his line of contender/hunting bbl's & setups. They were ment to be used in 14" contender bbl's on medium sized game.