Interesting nomination.
In order to do this, I don't think any meter - other than, perhaps, the ProTime meters, would be able to do the testing. The InRatio, CoaguChek XS and, supposedly, the Coag-Sense all ask for blood taken within fifteen seconds of making the incision -- that's because these meters factor in clotting agents that are in the skin. Only the Protime wants you to discard the first drop.
With the ProTime meter, it's conceivable that an IV can be used to extract enough venous blood for testing every few minutes. Of course, I realize that your suggestion takes the idea of testing to the extremes of absurdity. Even if the blood from my heel, perhaps, gives me a different INR reading from the blood in the fingertip, I don't think that there will be much that can be done about it as far as dosing is concerned.
Still, I wouldn't be terribly surprised if we aren't able to do an INR test - perhaps even non-invasively - with our smartphones a few years from now. I can take my pulse by touching a fingertip to my phone's camera lens; my phone can watch my eyes while I read from it and can determine when to go to the next page; my phone can also (supposedly) sense my hand motions when I move it above the screen. Perhaps someone can figure out a biological indicator that can reflect INR just by watching something on or below the skin's surface. (The InRatio and CoaguChek XS detect INR using amperage changes when blood and reagent mix - they don't look for actual clots). If, at some point in the future, we CAN test INR non-invasively, Chaconne's suggestion may actually become possible.
(However, I suspect that if there's a cheap, easy way to test INR without having to buy strips or a meter, the manufacturers of meters and strips will probably move pretty quickly to squash this)