Doc, I thought it would strengthen it.
No good?
Good question, I don't know if it would strengthen or not. Having said that, I've never seen a need to do it.
It looked like your reverse twist cordage in the earlier picture was quite good. And like Pict said, once you learn how to splice, the sky's the limit.
My personal perspective:
I know of 3 ways to splice - one is to fan out the end of the ply you want to splice in to and fan out the end of the piece you are adding on, kind of mesh it together and continue twisting. IMHO, this method sucks. (My apologies to Tom Brown Jr.)
Second, is to take the material that you're adding in, bend over the end so it looks like an inverted 'V' and lay this on the the fork of the 2 plies of the cordage you are splicing to (assuming the orientation of the cord you are making is vertical and the end you are working on is at the bottom). The short section of the inverted 'V' goes on the side that doesn't need to be spliced and the long section on the side that does, and then continue on cording. While this makes for a very strong splice, it increases the diameter of the cordage at the point of the splice. For a lot of applications, that wouldn't matter, but for something, say like a bow string............ (Doc shudders

) it adds string mass and looks ugly as hell.
The third method, and my favourite is:
As you are reverse twisting, you will feel with your fingers, when one or the other, or both, of the plies
starts to get
a bit thinner. When this happens, you take a
small amount of fibres (to make the diameter of the cord consistent), lay them on the ply that is becoming thinner with the end sticking past the main body of cord (this can be cut off later) and continue reverse twist cording. This type of splicing looks very much neater and because you are, in effect, continually splicing, there is no one weak spot.
When I am making cordage, I usually hang small (in diameter) separate pieces of fibre beside me and add them in as needed.
The foregoing was a little difficult to explain, so if you have a problem understanding it, say so, and I will either make some diagrams or take some pictures, unless somebody else has some pictures they can post.
BTW, (IMHO, of course

) my favourite method is also the easiest.
Doc
(Edit): I forgot Pict posted a link to a video he made, so he may have already covered the above. I didn't look at his video because it takes forever to download videos (High speed
lite 
) so if he did, my apologies.
Doc