Three recorders in Kunsthistorisches Museum Wien, SAM(Sammlung Alter Musikinstrumente)130, 140 & 148, are very unique. They look like Renaissance recorders, however have the similar function of Baroque recorders on the tessitura and the fingering. Their details are referred to in [1]. One of the authors of [1], the famous recorder maker, Adrian Brown mentions these three recorders in his HP[2] as follows;
"This experience led me to a trio of anonymous instruments hitherto undocumented, which bear a makers mark with an unusual motif, reminiscent of a pair of apples. These three recorders have proved a good basis for a late renaissance model with baroque fingering. The three instruments are: a soprano size, inventory number: SAM 130 in modern ch, and alto, SAM 140, a quarter-tone sharp of modern fhe and a small tenor, that suffered baroque gremodellingh, SAM 148 a quarter-tone sharp of modern df. These three instruments have fairly similar bore profiles to the gRafih models, except that their actual diameter is proportionally much greater, and surprisingly they play a full two octave range, using the fingerings given by Jambe de Fer and Van Eyck. On the other hand, their voicing and blowing characteristics, seem far closer to baroque instruments than the Rafis. The unusual interval between the three sizes may suggest that their original use was intended more in a solo than a consort capacity."
I don't know whether Jacob van Eyck knew this kind of recorder or not, but I believe this might be one of solutions for his 'Der Fluyten Lust-hof'. And, for diminuation music, Ortitz, Bassano, Virgiriano, etc, and for Italian early baroque music, this kind of recorder may help you with this tessitura and fingering(never trumpet sound!).
[1] Beatrix Darmstaedter & Adrian Brown "Die Renaissanceblockfloeten der Sammlung Alter Musikinstrumente des Kunsthistorischen Museums", Wien 2006, ISBN 3-85497-081-1
[2] https://adrianbrown.org/dolcimelo-recorders/