Karen, there is a real easy way to check on the value of this. Get the price for the contractor to strip and refinish the cabinets. Then make up a drawing of the space and kind of cabinets that you have and get pricing for comparable cabinets from a home center and from a cabinet making company. Try to get as comparable as you can, for now. I'll bet that the numbers will surprise you.
While you are calculating, add in the number of days that your kitchen will be "out of service". I don't know if that will be a factor for you, but that might surprise you also.
I'd really like to hear your experience on this. I'd tell you more about what I think but would like to hear your findings on the real facts first.
"Linear feet" are just feet that are measured in a straight line. The word "linear" is thrown in to impress the locals and keep the number separate from square feet or cubic feet. People doing trim work and laying pipe, among others, are justified in using the term "linear feet".