Shafts breaking

Things tend to bend before they break (on their own). Have you checked the struts and cutlass bearings? Maybe put a laser to the shaft?

20 x 20 four blade? Factory? 1.25" shafts & 350HP, all on the same cruiser?
(With or with-out mother in law on board?)
Your reduction must be at least 1.5:1,, maybe 2:1.

Have you contacted Carver asking what the real factory set up was? You may have to much prop.

MFGs use just what they need to sell a boat as cost reduced as possible. In your case, they pushed a bit more for the buck than for the long haul.

Also have to ask; how much shaft between the strut and engine or between the struts?

What safety factor or shaft ratting are you ordering for your replacement shafts (A22)?

From my days running large block Chevys (LBCs) in open fish boats, and a sport convertible, I can tell you, I would question the use (as you are now) 1 1/4 inch shafts with that set up.

My old 31 BlackFinn had 1.5" shafts, behind 400HP LBCs.
My 34 Pequod had 1.5" shafts, behind 340HP LBCs.
I worried about them but they never failed.

IMO, Applying 300HP on those low slippage props can easily make 1 1/4" cork screws.

As Capt Ralph says, need more info here. What type of material are your shafts? What is your gear ratio? Where are the shafts breaking? The usual place is at the start of the taper just forward of the props. Then you can plug into the shaft calculator to see what it says. You might be able to stay with 1.25" but use a stronger alloy if needed. Or you may be able to go up to 1.5" by using thin wall cutlass bearings in your existing struts and stern logs. The AQ22 high strength alloy is quite a bit stronger than AQ17 or AQ19 which might be what you have original from 1997.

Get a good prop shop to run calculations and determine the safety factor. Shaft material vary and as Dockmaster just mention you may need to upgrade the material. AQ22HS Is much stronger than others.