If this is a clock project, why not use an external RTC. Yes most can supply a 32.768kHz signal, but that's just using it as a TXCO, when it has all the time, date, alarm, etc. functionality built in as well. Another option is to just use the chip (DS3231) as in the Chronodot or one of its siblings (DS3232, DS3234). They're not cheap, $9 or $10, so by the time the backup battery and all is added, it'd probably cost as much or more as the Chronodot.
Here's my blog post on the experiment I did, I just stuck the crystal in the breadboard. I don't remember checking accuracy, but if it was way off, I would have probably noticed. But it was strictly an experiment; it worked and I didn't worry about finer points like accuracy. But yes those breadboards do add some capacitance to things. But the tape business sounds pretty sketchy as well 