Yes, I had the same problem with an M42 I had. I changed everything. Rule#1. Always do the easiest and cheapest fix. Try bleeding first. If that fails diagnose over heating issue. Stat, 2nd cheapest then pump. Well at least your cooling system is fail proof now...lol
park the car on a slope with the noise facing up. run the car to op temp put the heat on full defrost and then crack the bleeder nipple open. if you get nothing, rev the engine a bit higher then idle (1500rpm) to force the air to the highest point. You should start to see some flow with bubbles. Bubbles or spattering is air in the system. A constant flow is airless. Repeat the process a couple times. Close system and test drive. If the problem continues; repeat the process until it stops. If by chance it doesn't stop which happened to me. I pulled the car over; waited and removed the cap to release any air that may be trapped. But I waited for the car to cool before attempting. So be careful not to scold yourself with hot coolant. just keep repeating the cycle until it stabilizes.