Much of the information given here on the "Bf 109Z" is false, or at least highly distorted.
Many respected sources recount the twin-109F prototype that got bombed before it could fly (for example William Green's Warplanes of the Third Reich), but that now has to be cast in doubt.
According to Dan Sharp's research into original archive documents (Luftwaffe:Secret Designs of the Third Reich, Mortons, 2018. Pages 108-115), the relevant "schnellstbomber" programme began in May 1942. Several manufacturers submitted designs.
Messerschmitt first studied a composite Zwilling made from parts of several production types: 109 fuselages, 110 outer wings, Jumo 213 radial-engine power eggs. Many variations were subsequently considered in brief, some with 109 wings and/or other engines. Some even had a central 3-crew nacelle (depicted with rather loose imagination in an earlier post). Sharp does not note a big-gunned version, also posted earlier, and as this was a programme for a fast bomber, it seems highly unlikely. All retained twin production 109 tails.
They soon focused down onto Me 109 and 309 variants, wind tunnel tests resulting in the centre section being narrowed and the rear fuselages being joined by a single central tailplane fitted in place of the four conventional ones. The engines reverted to the 109's traditional inline.
A production design eventually emerged as the Me 109Zw (NB no longer Bf, due presumably to changes in the design office), based on two 109G airframes with a new centre section and the main undercarriage moved a little closer in towards the centreline of each fuselage. But Messerschmitt lost the competition. The Me 109Zw was dropped early in 1943, in favour of what became the Dornier Do 335 Pfeil. Subsequently, it was referred to as the Me 109Z.
Throughout, the competition phase was a paper exercise. Sharp documents it intimately. There is no discussion of an interim 109F based prototype. According to the many other respected authors, this would have been under construction throughout the period of the schnellstbomber competition. But it makes no sense; why would Messerschmitt be pursuing a direct parallel path for almost a year without it ever being mentioned in meeting after meeting? This would not be the first time we have caught the mainstream authors swallowing an unsubstantiated tall story, so on balance I believe that the 109F based prototype is a myth.