I've used most of this route at various times apart from short sections around Bridgwater but I expect they're OK. I think this offers an easier crossing of the Mendips by using the Shute Shelve tunnel (it has some lights but it's easier if you take your bike lights!) and an easier access to Bristol by using the Festival Way. It might be fun to take your bike on the train down to Taunton and ride back to Bristol.
Last time I used the three main rough sections of this route (alongside the canal in Taunton, the Strawberry Line and the Flax Bourton Greenway), all three were OK stonedust and level or gentle gradients. If you want to choose the spectacle of climbing over the Mendips or entering Bristol over the Clifton Suspension Bridge, go for it, but I think this is an easier option and has its own beauty spots.