Hello fellow land of cold chop inhabitant. The primary issue here, I suspect, is that the Mad Dog is a "performance shape" (according to the Naish website) and the 29" width is the main cause of your stability woes. The Naish website also suggests that the board is suitable for riders up to 90 kgs. You at 86 kgs + a wet 5mm wetsuit + booties + gloves will likely be around 90 kgs. So. this means you really have to be on your game with fitness and technique because you are at the top end of the suggested weight range. 121/90 is 1.34, so in the top end intermediate / advanced band according to the Guild factor.
Technique is mostly around how you paddle and how you stand when waiting and paddling for waves. Considering that you only get on the water around twice a month, you are doing well. I always have a better session with a high wave count when I feel stable as I am repositioning in the lineup and paddling for a wave.
I would think that a board like an 8'7" Starboard Wedge already suggested here would be an ideal choice for you with its wide and stable shape, yet still allow for the progression that you are seeking and I am not saying that only because I am an SB fanboy.
However, you didn't mention details of how you currently stand and so forth when paddling into waves, so you could also look at your technique. I went to Bantham last Wednesday and the conditions were pretty great. There were quite a few fellow SUP surfers in the lineup and I was surprised that all of them were paddling around in parallel stance. I am always in full surf or semi surf / fence stance, depending on the board and I have no idea how one can feel comfortable, or stable, standing in the surf in parallel stance.
Have a look at this thread, particularly supthecreek's and colas' replies, for some great tips on how to improve your stability when paddling into waves
www.seabreeze.com.au/forums/Stand-Up-Paddle/SUP/How-do-you-like-to-stand-when-paddling-for-waves-