There have been a number of attempts of determining a means of estimating the CE. Methods by Cruz-Orive and Braendgarrd and Roberts aas well as others have been largely passed by with the Matheron transitive method.

The Schmitz-Hof method is basically a pair of values. That makes little sense. The range is so wide so as to be useless unless the larger value is used. That worst case is exactly the CE based on independent random sampling. That does not apply. So maybe the smaller value should be used. The formula is based on curve fitting and not a derivation. The curve fitting was done by collecting data from a few simulations.

I would stick with what has been derived. The derivations have been done and redone in Australia, France, Spain, the UK, Denmark, the US, and plenty of other places. You might want to read or gloss over the comments in:

Cruz-Orive, L.M., García-Fiñana, M., A review of the article: Comments on the shortcomings of predicting the precision of Cavalieri volume estimates based upon assumed measurement functions, by Edmund Glaser, Journal of Microscopy, Vol. 218, Pt. 1, 2005, pp. 6-8

These few pages point out how proponents of other methods are missing the basic idea when it comes to the practical and theoretical concepts involved in this work.

You also might find it instructive to look at Scheaffer's book Elementary Sampling Theory. You need to get the 1990 edition. Look at chapters 4 and 7. You will see that he lists the important assumption that the samples are independent of each other. This is an easy to miss assumption.

I ran some simulations testing some of these CE formulas. I find that the m=1 (the 1/240) estimate is usually a slight underestimate of the CE. The Scheaffer method is way off. The Schmitz-Hof has such a large range as to be of no practical value.

Last but not least think of it this way. You are working on a project. You want to publish. Do you want to defend your biological work or do you want to defend a statistical method not adopted by your peers in your field of interest? That might happen if you decide to use an alternative method. The Matheron method is today's standard. I would go with the flow.

Good luck with your work. The fact that you are taking the time to learn about all of these different ideas suggests that you are going to do a fine job.

Cheers