I'm not sure a frequency counter is a device designed for fancy experiments. Well, this thing is big. But if the requirement is to measure something that is within its spec, the good chance is that it will quickly become apparent that it's more convenient to do so with the old professional equipment than using a modern home entertainment device in shiny plastic box.
Also, no matter what the internal padding is, the enclosure itself is a thing of high value. It'll be a major enterprise for an individual to design it, to prepare all the materials, to find a casting service, a machining service, a painting service, etc., to manufacture something of that quality from scratch. And it will not be cheap anyway. A good pre-built GP housings of that class are also not cheap. This is a real metal thing that is closer to build-once-use-for-life model than modern tech toys, which becomes obsolete tomorrow, so it'll make sense to re-purpose the cabinet for whatever you want.
Thanks for reading. I admit I also could not find a standard quality wiring diagram. The best of my findings:
http://rcl-radio.ru/wp-content/uploads/2017/03/h3_34.pdf (UM and theory of operation)
http://electro-tech.narod.ru/schematics/measure/freq/ch3-34/ch3-34.djvu (schematics)