Steve - most of the guys around here still using .303's for moose are using the Winchester 180gr Power Points & are very happy with them. This switch was made when the Imperial and/or Dominion 215 KlingKore SoftPoints (RN) were no longer available.

I have a close friend I chambered a .308" groove barrel for, using a .303 reamer with the pilot ground to fit the .300" bore. He wanted this chambering so he could also use factory ammo in it. The factory ammo did not shoot well, nor did the 220gr. Hornady's he wanted to use. Instead he found it a tack driver with Hornady 150gr. Interbonds, loading with full power loads of 4064 and 4320 IMR powders.

We put that barrel on a P-14 action and it now, aside from his 8x68S, it is his favourite long barreled (27") moose, deer and elk rifle - or at least seems so.

He is loading 150gr. InterBOND bullets to 2,750fps and is very happy with them on all 3 animals, taking only one shot each. The Royal Elk was the longest shot at just over 400yards. Keith is an incredible game shot, btw, is more than a bit famous around here for that prowess.
He noted every bullet was perfectly expanded, no breakups and decent penetration. His whitetail and mule deer were closest shots at just over 100 yards.

Good luck. If I was loading for a .303, I would likely use the 180gr. PP if it was available here. So far, it is not.

My only .303 is a Mark 1 #4 Enfield I re-chambered to .303 Express.(necked down .350 Rem Mag case) I have tested some 174gr. Hornadys loaded, and have some 180gr. steel jacketed Normas loaded also for testing.

The 174gr. Hornadys ran 2,940fps and 1 1/2" at 100 meters with the battle sights, however I expect they might be too soft for that speed. The barrel is a new one, but is 2-groove & .315" groove to groove. The rifle was sporterized and sold by Remington.
The 180gr. semi-round nose Norma boat tails might actually do better on most game.