As far as extracting the tooth with your leatherman goes, it would solve the problem, assuming you were able to get the WHOLE tooth, intact or in pieces. However, that may be problematic depending on which tooth and the condition of the tooth structure. I spent four years in the AF assisting dentists and even when the doc is an oral surgeon with years of experience in extractions, using all the best tools for the job in a well lit environment and an anesthetized and therefore not writhing patient, breaking off one or more roots is not a rare event especially if the original cause of pain is due to the tooth having decayed to the point of nerve involvement. In that case (rotten tooth) the breaking of the tooth especially when using pliers is almost guaranteed. In a dentists office this is not such a big deal as the proper tools are available to remove enough bone to be able to retrieve remaining root pieces. I don't have an answer to this dilema as the variables like condition of the tooth structure, which tooth (the further back in the mouth you go number of roots increase to 3 or 4), shape of roots (some multi root teeth have roots which curve sharply and in different directions making removal without something to cut away bone, impossible). Ignoring the pain for very log can be problematic too as, depending on tooth location, left alone long enough the position of some teeth make it possible for the infection to spread to the brain eventually. I wish I had some sort of solution to contribute but I don't, just thought some of the risks should be mentioned.