I have not used this method, but I've seen references to it for quite a few years. If you have a non-critical tape to test with, start there.
If your tapes have already deteriorated to the point they are flaking, and the residue is clogging the heads on your tape deck, you may have larger problem than just cleaning them so you can archive them. Given their irreplaceable nature, I think you would be well advised to find a professional archiving service that specializes in restoring old magnetic tapes. I recently did this for a batch of old magnetic tape voice recordings of family members who are long gone, and I'm really glad I spent the money and had it done right. (I also had professional company transfer a bunch of 8mm home movies made in the 1940's onto videotape and CD-ROM, added a soundtrack, and gave them for Christmas gifts to the whole family.)
If you botch the cleaning job, the tapes may be ruined for good, so do it right the first time.
I couldn't agree more with Scott on this and strongly urge you to follow his advice. I, too, had a similar issue with some audio tape and, later, some old 8mm home movies. After partially ruining one audio tape of my grandmother singing in a wedding during the 1940's, I had all the rest done professionally. It was a bit "pricey", but ask yourself how important the tapes are to you. Next, estimate the cost you'd pay someone for these tapes if they didn't already exist. I'll wager that the price would be much higher than the restoration. Good luck. If you live in the Bay Area (CA), e-mail me and I can give you a couple of good sources for the work.