This exact thing happened to me when I blew my rear turbo in May of last year (z4 e89). Downpipes with cat delete and stock exhaust behind that. Everybody gave me the same advice (take the exhaust off and stand it up to drain, flush with cleaner, run it hard for a while to let it burn off). Well, I did all of that and it never cleared up and it continued to smoke when it got hot. So I took the rear exhaust off and cut the skin of the muffler to access the internals.
I'm glad I did - because of the configuration of the dampening material in the muffler, there was about a quart of oil/sludge trapped between the two sections of silencer material. Both sections in the exhaust were completely soaked with oil/sludge and there was no way that would have "burned" off.
I removed all the old silencer material, cleaned, and wrapped some ceramic fiber insulation around each of the perforated pipes to cut down on the noise a little (stainless steel tie wraps).
I re-welded the skin on and reattached .... and voila, no more smoking.
Sound is a little more deep from that side, but it sounds so good, I'm thinking of removing the other muffler and performing the same modification to improve the overall sound.
I hate to tell you, but from experience, I don't think it will ever "just burn off." I really think the only way to get rid of it is to remove the old insulation and replace.