Solution for desk chair on an uneven floor
I would think that the plastic chair mat would work well if you used it in conjunction with some type of padding under it. A piece of short pile rubber backed carpet that was trimmed to the same size as the chair mat would bridge the underlying uneven joining strip.

In my work lab I use these plastic chair mats to cover the whole carpeted floor (four mats laid side by side / end to end). They rest in a short pile carpet and have been in use for 12 years now. Only in the last 3-4 months has one started to crack. 

If you get the type of clear plastic mats that are made from a flexible plastic they will hold up longer than the very hard dense plastic style.