One of the things that might be confusing the OP is that the Tropopause is that it does change height. The STANDARD ATMOSPHERE MODEL shows the Trop at around 36000ft. In actuality it changes:

The tropopause height does not gradually drop from low to high latitudes. Rather, it drops rapidly in the area of the subtropical and polar front jets (STJ and PFJ respectively in the Figure on the left), as shown in the Palmen-Newton model of the general circulation (Fig 12.16 or Fig on left). Especially when the jet is strong and the associated front at low levels intense, then the tropopause height drops suddenly across the jet stream. Sometimes the tropopause actually folds down to 500 hPa (5.5 km) and even lower, just behind a well-defined cold front. The subsided stratospheric air within such a tropopause fold (or in the less pronounced tropopause dip) is much warmer than the tropospheric air it replaces, at the same level, and this warm advection aloft (around 300 hPa) largely explains the movement of the frontal low (at the surface) into the cold airmass, a process called occlusion.

The height of the tropopause

So, the apparent problem of the Trop layer being static should not be assumed. Use the formula and forget the standard trop level. It's like the 15 Deg. C / 59 F value. An assumed standard only, used for the basis of reference, not an in-fact condition most of the time.