Andy, you'd be surprised what museums don't know about their collections. I worked in aviation museums for nine years and made some rather surprising discoveries about things within their collections that they themselves did not know.
Having posted the same question on 12 O'Clock High I found an answer awating me. Yes, 3C+BA (AM.15) was flown by Schnaufer to be captured by the RAF, but was not originally Schnaufer's Bf 110; the original 3C+BA was destroyed on the ground at Eggebeck. Schnaufer's last mount was G9+EF, which was not captured. So, 3C+BA that was captured by the British was in fact G9+DX and was painted up as such on Schnaufer's request, so Butler and Scutts are correct; that aircraft was not Schnaufer's but an imposter that Schnaufer had flown and had marked up as his. This information was provided on 12 O'Clock High forum by forum member Wim, whom needs no introduction to those with any knowledge of Schanufer. He also posted Flugbuch entries on the matter.
He also stated that the AWM image showing G9+BA as posted above is correctly identified; this was confirmed by Flt Lt Langworthy, whom Wim interviewed at a later date and can be seen at far left in the image. He also states that the fins that survive in Australia and London are from this aircraft. Mystery solved, then!
So, to assess. Schanufer's usual mount was G9+EF, but there were two Bf 110s that were painted up as Schnaufer's on his request, and although he flew them, they were not his usual aircraft and did not fly combat ops in them. These are G9+BA and G9+DX; the latter was painted as 3C+BA and became AM.15 and the former is where the surviving fins in museums are from. One of G9+EF's fins survives in private hands.