For some time I have thought about a sturdy tripod. Most definitely not a travel tripod!
It turns out I had most of what I needed to accomplish this on a budget.
I have a few land surveyors tripods. These are, of course, designed for precision land surveying work, so as sturdy as can be while still being portable.
From a friendly local Land Surveyor, I obtained some used equipment he no longer needs. A tribrach and a tribrach adapter. The tribrach is the grey device that mounts to the top of the tripod. It is designed to provide leveling and a secure mount for variety of survey gear such as a theodolite, a total station or similar. The black part, that fits securely onto that is called a tribrach adapter. It is used to fit a prism or other survey attachment to the the tribrach. I removed the tribrach adapter centre screw and fitted a bolt with the correct thread to mount a tripod ballhead.
The ballhead / tribrach adapter / tribrach combination is heavy enough to use on it's own as a small table top tripod and supports the K-1 II and battery grip with ease.