I don't think you need a "Zuverlässikeitsüberprüfung" when flying German registered aircraft with your Spanish licence. At least I can't find any such provision. For what it's worth, there are a number of German pilots who changed their German licences to Austrian ones just to avoid this German travesty in the first place.
Even when you start training in a German flight school, there should be no requierement for you to get a "ZÜP". According to sec. 16 para. 2 of the German Ordinance on Aviation Personnel (Verordnung über Luftfahrtpersonal - LuftPersV), only those students applying for a licence for the first time need to submit a copy of their "ZÜP" to the flight school.
With the help of Google Translate, you can check the applicable regulations yourself. German federal law is published on
www.gesetze-im-internet.de. The requirement for the "ZÜP" follows from sec. 7 para. 4 of the Aviation Security Act (Luftsicherheitsgesetz - LuftSiG).
https://www-gesetze--im--internet-de..._x_tr_pto=wapp
https://www-gesetze--im--internet-de..._x_tr_pto=wapp