Yes I have tried the E80F tube, though not the Heintze & Kaufmann version, but two versions made by Telefunken: I tested the long- and the short glass body versions (yours is the long version, the short version's glass envelope is identical in dimensions with that of the EF86 and EF806S made by Telefunken).
During the design and early production phases of the Brauner KHE (Klaus Heyne Edition), I considered that tube type, as an alternative to the EF86, and made long-term tests. Conclusion: all E80F draw slightly larger heater current, and power supplies needed to be adjusted accordingly. The long envelope version had a distinctly different and unpleasant midrange behavior- it was constricted, congested and plain harsh sounding in the mid frequencies, and in my opinion, unusable in a high-end microphone. (I never tested the Heintze & Kaufmann-made version you show in your pictures.)
However, its shorter envelope sibling, also made by Telefunken, and also with gold-plated pins, was excellent, and its performance on-par with the best EF86 I had used. It had very appealing, fast, frequency-balanced, audio, was super quiet, and, aside of one replacement in 10 years, has held up well in all the KHE mics it was initially installed.
It would be a good idea for you to compare the sound of the long-body version in your mic to a short-body E80F (if you can find one) or a very good, preferably Telefunken-made, EF86/806S, to ascertain whether my observations about the different tonality of the two sizes (and differing construction of anodes and filaments) in that tube are also experienced by you.
Best regards,
KH