I don't know if you are aware but you can buy through Advance tickets across London eg- Canterbury to Lowestoft or Lowestoft to Plymouth (just as examples).
Such tickets include your cross London transfers by tube/DLR. Although they are on specific timed trains they are also protected connections in that if the first train is late (or the tube has problems) you can automatically take the next service for train two. So to Plymouth that would be one hour later (normally).
And Two Together discounts apply, subject to the normal time restrictions.
It all depends on how much you value flexibility, and what your reaction is to stress, if the trains do have problems. I'm not sure what the price is of an All England Brit rail pass (can't see the prices here in the UK), nor am I certain how much searching out the very best deal, to save a few $ or cents is important to you.
But on the face of what you have written above my gut reaction is that Britrail is the best solution for you personally. Even if it doesn't work out as quite the best deal then in the overall context of the cost of the whole trip there isn't going to be a significant difference.
Yes with Britrail you will have to pay your tube/DLR fares in addition. Not a big deal.
If you take that decision don't then go back and check the cost of your trips, and find you might have saved £34.56 (or whatever) overall. Take the decision and move on.