invisiblehand, thanks for the info. I have a 2009 model Mini with a 2008 model handlepost.
This thread tells me that the Mini uses a 114x68 bottom bracket. Not sure how common that size is. The Shimano UN54 BB is available in 113 or 115mm, not 114. Given that the chainline on the Mini is not perfect, perhaps a different width would be an improvement. As for the headset, I won't be doing this frequently, so good advice to take it to the LBS.