Pete, Since 2014 I've averaged 10-12 weeks in Scotland and concentrated that time on the northeast coast near Dornoch, Golspie, and Brora. I don't want to contradict any of the other long term visitors or residents, but my experience has been that the Scottish weather can be fickle indeed. Trying to assure oneself of good weather is a sucker bet. That being said I think the August and September period is likely to be the most consistently good. David Tepper splits his time between late spring and late summer and so can chip in with his experiences/opinion.
The east coast is cooler and drier than western Scotland, and I'm told that Dornoch has something of a microclimate that insulates it from some of the fouler weather that afflicts areas just north and south of it. As I say I'm told that and can't swear to it.
Golspie is so close to the North Sea (formerly, prior to World War I at least, know as the German Ocean) that there is little buffering effect. Part of the course is no more more than 10 yards from the water at high tides. Sadly, there were some exceptional tides in recent memory that flooded the course. I play most of my golf at Golspie and I think the wind is more of a constant factory there than at either Dornoch or Brora. The opinions of others may differ and the facts might as well if there were any way of ascertaining it. Overseas membership at Golspie also provides reduced rates at many courses and at 225 GBP provides a one time payment that is the equivalent of four rounds at full price. You might want to look into it.
As far as moving base, there is only fifteen miles between Dornoch and Brora (and going south Tain, a very enjoyable course is only ten miles). I like settling in rather than moving, but your attitude may well vary. Either option provides ample opportunity for getting in a lot of golf. And as you say there is lawn bowling aplenty. I think Tain may have lawn bowling as well.
Accommodation advice is dependent on whether you want to go the B & B route or whether you prefer full self catering. Both are available in the area.
I hope I've provided something useful in the midst of the caveats, but if you love golf, especially links golf, I don't know how you can go wrong in this part of the world. Dornoch may not be exactly Brigadoon, but it's damned close.