Any tricks to extend laminate floor without having to re-lay the whole floor?
Well you are lucky because of those patio doors.  What do I expect to see by patio doors - TILE!

So:


Go out and find some faux travertine (or the real stuff) tile.  It looks like you need some 12"x12"s.
Measure 24.5 inches from door all the way across.
Cut out laminate with circular saw.  (several saw types will work here)
Glue a tile edging strip about 1/4" from laminate (this may be the bottom holder of a transition strip but that's another question)
Mix thinset.
Install tiles.  You should only have to cut the two tiles on the far right.
Wait a day for thinset to cure a bit.
Grout.  You should have a spacer by door, middle, and before transition holder.
Clean up area.
Glue down transition.


Pros:


It will look nice.  You could even put a third row in here.
Depending on tile it could cost less than $150.
The tile will transition to the door much better than the laminate.  There isn't really any kind of good trim to put by the door in your situation - it is a common question on this site.
Your laminate seems to have long runs.  The transition should give it some play.  
It is like 3-4 hours of total work.