You already have a fork brace on your R65, unless a PO errored and removed it. It's that heavy steel part under the front fender.
As far as rain groove induced wobbles, some tires do and some don't. I have Bridgestones Spitfire S-11 on both R65s and my R100S. The few times I've ridden on grooved pavement, there has been no noticable twitching.
Are your steering stem bearings greased and properly adjusted with just a smidge of pre-load? The swingarm has the same bearings and they also require a little preload. Either or could induce the wobbles.