My personal preference is actually riding nowhere near the road if possible - until we moved office my cycling route to work crossed a few busy roads but had very little riding along roads. It was all cycle paths, some through a park and some on a wide shared pavement, a decent distance from the road (and thus traffic and fumes)What the routing like around the narrow bits? I take the longer route into work on the bike to avoid the wider roads due to faster speeds cars travel at. On inherently narrow roads the speed of traffic is actually much slower. My personal preference of bike commute routes is unclassified road > narrow B roads > wider B roads > Trunk roads.
I 100% avoid any kind of multi lane trunk roads unless its literally for a few seconds to join smaller roads, the wider the road the more dangerous it actually is in my experience as drivers tend not to focus and will wonder across lanes without checking.