UPDATE. Almost exactly one year later, the SII finally landed in Santa Rosa where it will be checked out and evaluated. Regarding the electronic noise, after talking to Mica over the phone, a few months back, I explained how the neck pickup was missing 2 screws and that it was laid almost all the way down. Mica suggested that that could have been the reason why it was producing the hum and graciously sent me a few replacement screws (along with a lovely big sticker) for me to raise the pickup to a reasonable height. Well, the hum decreased quite a bit bringing it to a more acceptable level, similar to a typical single coil in a Jazz Bass and always changing based on the direction of the bass. Hopefully this can be fixed without having to replace anything but the last word will be up to Mr Ron.
Regarding the rest, refin or not refin, the jury is still out. The Omega cut and the 2 'nice' dings on the back of the neck need to be addressed for sure, then we'll see what else...