Jcanracer - in my experience the difficulty arises when a wave picks you up and surfs you in and no amount of rudder is going to be sufficient to counteract the turning power of a boat that is being flung shoreward by a sizeable wave. It is not the rudder that causes the boat to start turning but the effort of the wave pushing the boat from behind the point of resistance - once the boat gets off line it will start to turn and very quickly the turning becomes irresistable... and usually you end up being rolled.
I recommend that you practise techniques for preventing waves from pushing you in by slowing your boat for each one that comes up behind you.
In smaller waves this can be done with your paddle with a reverse stroke.
As the waves get a bit bigger you need to hang your feet over the sides of the boat AND use your paddle in reverse.
The bad news is that waves can get so big that it is impossible to prevent the boat from surfing with just paddle and feet. For these conditions I have three different tactics: 1. Don't go out in big wave conditions; 2. Don't return to shore on surf beaches, and 3. Carry a small series drogue to chuck out of the back of the boat before pedaling in through big waves. The latter solution works extremely well but you have to remember to carry it, know how to deploy it and, most likely, have it already set up for use which is not always convenient so I tend to rely heavily on 1 & 2
Either way the larger rudder may go some way towards helping maintain directional stability during some surfing re-entries but it should not contribute to making your boat more likely to turn & roll... unless you have not got it centred (and a passing wave can and will want to knock any rudder about a bit) which is yet another thing to attend to in the ~1.5 seconds during which your re-entry goes from yay! to nay! so I always lift my rudder before coming in to shore.