Im less about rules of thumbs than theoretic approaches.
You achieve higher Magnification by going closer. Using a macro lens or extension tube allows you to get closer and still be in focus. It is the increased magnification that makes any blur more visible and that is the source of your statement " this rule breaks down".
Another way to achieve this higher magnification is by using longer focal length. This longer focal length could be estimated and used in the "rule of thumb" formula.
Lets take an example 50mm lens. Typically they have maximum magnification 0.15x. This is at minimum focus distance, which is not the general distance to use it. Rules of thumb are based on normal average usage. the 50mm is typically used for body-shoulder portraits. let's say 3 meters distance. you can now calculate the magnification on a fullframe camera (the rule of thumb was made for 35mm film!):
M= 0.02 (or 1:58 to be accurate)
For macro you have M=1 (true macro) some macro lenses have only 0.5x and still call it macro. that's fake!
To get to 1:1 you need to multiply by 58. Thats focal length you need to multiply by 58 to get the same magnification. in your timing 1/f*58 . so your 1/50s on fullframe becomes 1/(50*58) = 1/2900s. On crop you need to 1/(2900*1.6). That doesnt sound so bad, if your camera goes to 1/8000.
But notice that for the extreme narrow DOF you need to use a small aperture, too. this needs a hilarious amount of light.
So in conclusion, I strongly suggest you do not handhold the camera for macro with narrow aperture without strobe.
If you have IS you divide by the power of 2 of hte number of stops it is supposed to give you. So a 2 stop IS becomes 4/2900 = 1/725s. a 4 stop IS is 1/181s. Now it starts being easy to use again.
And note that this is to get the equal safety in shooting nonblurry as the rule of thumb gives you . it is certainly possible to get nice shots going below the rule of thumb, depending on your steady hand and chaos in the situation.