Is sound quality effected by twist connecting 2 speaker wires together for extra length?

I would crimp them with copper sleeves. A good crimp shouldn't oxidize on the cold welded contact surfaces. You could then wrap with Teflon plumber's tape and put some heat shrink tubing over it and it should be good for a long while..

Twisting and securing with cap of proper gauge or using brass crimp plates will work better than soldering.
spray from time to time with Deoxit to prevent corrosion.

This is really one of those questions that can't be accurately answered by anyone other than yourself. I could say outright that I think that I would hear a difference, but in reality maybe yes maybe not. The point is that only you can answer to your satisfaction whether there is a notable difference. I have discovered over the years that we each hear and perceive what we hear differently.  What I would venture is that you would hear a more significant change with different cables rather than adding 2' of 12 ga onto existing 12 gauge speaker wire.

I am in a similar situation.
I have two different systems coexisting in my living room; The difference is that I have 2 amplifiers and 2 pairs of speakers. All these 4 "devices" are connected to a switch that allows me to choose which amplifier will be feeding which pair of speakers. I made this switch myself using only top quality parts and wire, and the result is the same as if there was no switch at all. I compared many times the final result to the simple solution of running dedicated cables from one amplifier to a pair of speakers, and I noticed no difference in sound quality.
Maybe some audiophile folks will say that it is impossible to achieve the same sound and that the switch must change the sonics and dynamics and all those exquisite words that describe good sounding music... But I'm not an audiophile and I don't notice any difference.
Regarding your cable situation, I don't think there is a degradation in sound by attaching two wires together. I already did it to connect a very old system to a pair of speakers (my dad's old Onkyo receiver to his Onkyo monitor speakers): the original wire was too short for the new location in the room, so I just added a bit more of the same wire - nobody ever noticed any change.
Personally I would prefer a single run. And also there are better ways to connect two wires rather than just twisting them together (by crimping unions or junction boxes, for example). But in the end, it's all good!
Actually I'm not a cable-believer guy. I have some expensive cables playing along with DIY cables and the difference isn't noticeable.
That's my opinion, I'm sure some will tell the opposite (and talk about the wire direction and the skin effect, etc...).

p.s. - if you look at my system photos, you can see my switch box. 

Thanks for chiming in, good info! 

How owe about the switch in that case? Should I bother removing it? Or would you say the switch definitely could effect the sound and should be removed?

I used to do it all the time. I never noticed a difference. If there is an effect, I believe it would not be noticeable. Some, I am sure, would say the flow of electrons is in some way negatively effected, or noise introduced into the line.  Once again, noticeably?

Someone must have some knowledge about the positive/negative effects of joining 2 short speaker wires together to act as 1 longer cable...

thanks in advance for any advice! :)