I asked BASC and this forum for advise for quite similar circumstances, as my stalking land starts some 70 yards from my home, and I have to walk up and cross a public road which is a dead-end single track dark lane, but still a public highway.
On other permissions I can cross from farm to farm by simply crossing some minor roads.
The answer was that I required 'good reason' to be on a public highway with a rifle that was not in a slip, and the rifle had to be unloaded.
For me, going from one field to another while stalking by crossing a minor road is 'good reason'. The home situation (70 yards walk) is slightly different but I have informed my neighbours who know what I do and nobody had an issue with it, again is is quite rediculous to carry my rifle in a slip for 70 yards on a very quiet very minor road and than have to hide the slip in the bushes to start the stalk.
I translate 'good reason' as 'is it reasonable' - the answer in your case is Yes.
Naturally you have to pick your moment for crossing these small country roads, maybe it is not such a good idea to cross when a group of ramblers happens to pass, or a Police squad car

, although you would be doing nothing illegal.