To get brass thickness in the case wall, I worked from a photo John posted on another site of a sectioned modern .44-40 case (which he was comparing to an early BP case without a solid head).
Bryan Austin provided here an estimate of the pressure John's load might have generated. His estimate of 7.2 ksi I adjusted upwards to 8 ksi to account for the heavier bullet and charge which John used in his test.
I obtained brass mechanical properties and friction coefficients from the site of Varmint Al, who did a full blown, dynamic, finite element analysis of a .243 firing in its chamber. (Al's simulation is porn for us mechanical engineers. He's a retired stress analyst from Lawrence Livermore labs.)
I estimate that at the peak pressure, the case to .4" from its base was capable of containing the peak pressure without assist from the chamber walls. Above that to the case mouth, I estimate the brass could on average contain nearly half the pressure, leaving the rest to be held by the chamber. The resulting cling (friction) would be around 1300 lb, but the net gas force rearward on the brass was estimated to be under 1000 lb. At that point (0.4" up) where the brass would barely be touching the chamber, there is enough brass cross section to hold 1000 lb without plastically deforming reward, unlike with Al's high pressure .243 Win.
The case walls being blown outward have much less inertia than the entire case moving rearward, so case cling will occur sooner than the base can reach the bolt. My back of the envelope calculation, then, says the cling could hold the case forward, and John's little clay balls wouldn't have been crushed, as he observed.
This is not to say there is no bolt thrust at peak pressure. John's test hints the primer produced a fair thrust on the bolt. Note that over the course of the firing, the primer moved inward in its pocket. Surely the primer's blast moved it rearwards to the bolt face (see Varmint Al's dynamic simulation), then gas pressure shoved the case rearward until cling arrested this motion. I estimated 300 lb of bolt thrust from the primer due to the gas forces acting upon it, perhaps more as the pressurized primer was being forced back into its pocket. (That the primer is a significant factor in bolt thrust can be seen in the analysis done by Varmint Al. However, Al's numbers suggest 150 lb might be a better estimate in this problem.)
edit: I want to emphasize the numbers I came up with are only rough estimates. The calculated spread between the gas force pushing the case rearward and the friction holding it to the chamber walls was not great. A certain amount of luck was involved in the numbers coming out in agreement with John's experiment.
![Very Happy :D](./images/smilies/icon_biggrin.gif)
It would be fun to see the results of strain gauges on the toggle links of an 1873 firing that mild .44 WCF load.