The few DDs germany build before and in WW2 were mostly bad designs with teething troubles.
However the alternative history of Enigma gives us a good solution for this problem.
In Enigma France and England are Allied with Germany (well, kinda) so it is only natural to use use foreign Designs which are superiour to the germans in the german fleet.
One example would be the french "Le Fantasque" Destroyers.
These large destroyers (2569 BRT) were build from the early till the mid 1930s and were mainly designed as a counterpart to the latest Italian light Cruisers.
Here are the technical datas:
Displacement: 2569 tons standard (3200 to 3400 tons full load)
Speed: 37 Knots (however the maximum speed achieved in trials was over 45knots!)
Compliment: 210.
Armament:
Five 5.5 inch guns (http://www.warships1.com/Weapons/WNFR_55-45_m1929.htm),
Four 37mm AA guns (http://www.warships1.com/Weapons/WNFR_37-50_cail_m1933.htm),
Four 13.2mm AA
(http://www.warships1.com/Weapons/WNFR_13mm_aamg.htm),
Nine 21.7 inch Torpedo Tubes,
50 mines
Source:
http://www.battleships-cruisers.co.uk/le_fantasque.htm
(and many more, just google for "fantasque destroyer")
Later in WW2 some of the ships were refitted in the US (and reclassified as light cruisers), one torpedo mount was removed (means 3 torpedos less) and the AA armament was beefed up to
8 Bofors 40mm (http://www.warships1.com/Weapons/WNUS_4cm-56_mk12.htm)
10 2cm Oerlikons (http://www.warships1.com/Weapons/WNUS_2cm-70_mk234.htm)
Source: http://mapage.noos.fr/4edmm/croiseur.htm
I would suggest to add this class as german destroyer with rank requirements just below the light cruisers.
This would give the germans finally a modern destroyer, which is not a WW1 design (the DD is even based on a 1906 light cruiser), which will be able to fight the american and alliance DDs or has the ability to run when fighting superiour forces.
Of course the Z-35c Babarossa should not be completly replaced, the Le Fantasque DDs should be placed like a less numerous state of the art destroyer leading the german destroyer squadrons while the Z-35c remains the backbone of the german navy.


Aren't they just beautiful?