I had a similar problem recently recording an accordion.
I was a recording a band with some loud and persistent instruments, so trying to avoid spillage I close miked the instruments using end-fire mics. This was using Rode NT3 - mid-price similar to AKG C1000s mentioned above. I prefer these mics to the AKG, they give a good sound, more signal and less noise.
Everything sounded OK except the accordion, which sounded particularly rough on the right hand - the reeds really came over with a rasping quality, quite unlike the real thing.
We tried a few things, but ended up backing the mic off by a metre, and repositioning the accordionist to reduce spillage from the other instruments. Once we had done this the accordion was sounding sweet again.
When recording solo concertina the spillage problem from other instruments does not exist. I usually use a pair of AKG 3000b microphones - large diaghram, mid price mics. Again backing off a bit, and placed on either side, slightly behind the player. This position gives two benefits - better separation (less cross-over in the stereo image), and less key noise (if the concertina has any rattly keys).
I learnt this technique from a professional sound recordist who was very experienced in recording accordions. Tried it out on the concertina and was pleased with the results.