Keep it. Like you, I too was brought up in the MG era. I had always wanted an MG. In 2006 I picked up a 2006 Z4 on an incredible deal. I gave up the Z4 in 2008. I was aggressively looking for an MG, but I could not pass up the Z4 deal. I now have a Z3 and love it. Just like the MGs, it is not perfect which is why I love it.
Keep the Z3, don't give it up. Drive it. Even in the winter. There are days in the winter that you still can drive it. Even possibly one day a week to work. Think of it as therapy. If you still have that thrill feeling when you drive it, you miss it if you give it up. When your kids are able to drive, let them too feel that thrill of driving it. If the Z3 is not a financial burden, have fun with it year round.
This is my toy. 1998 (2.8)