The Jayhawk Detox is the quickest, safest, and most efficient means of oil extraction. That is not an opinion, it is a fact, the testing has been done.
The OP specifically asked about the best method "for the money".
For the money it's going to depend on how many balls you own, and how often you bowl. For someone who owns 20+ balls, and bowls 20-30 games per week across said balls, the Detox may not be the most cost efficient method.
I can buy a heat bucket for under $200 (I did), and I can say unequivocally that it works. And it works safely if you stay within manufacturer heat guidelines. I believe it's still open to debate how much more effective Detox may or may not be. If I recall, you weren't able to quantify this when you first started using and recommending the product.
My bucket paid for itself over the first few weeks of use. If I want to use Detox, assuming I can find a shop that has one, I'll be paying $15-$20 per ball, since it's not an at home consumer product. That cost never goes away, and at least for me, would be a prohibitively expensive option over the long run.
For someone who bowls much less, and has no desire to own a personal revivor unit, Detox at a proshop might be an attractive option.