Obtain an FAA 61.75 piggyback on my now UK PPL which will enable me to fly N-Reg aircraft here in Germany, at a local US Army flying club.
Unless it's an annex I aircraft, you'll be required to hold an EASA Part-FCL licence (or validation) from 20 Jun 2022 if the aircraft operator is based there. Article 12(4) of the Aircrew Regulation as amended (in three days from now) by Commission Implementing Regulation (EU) 2020/2193 of 16 December 2020. Separately, under Commission Delegated Regulation (EU) 2020/723, art 8(3), member states have the option of granting a "light weight" validation (administratively similar to the US 61.75 airman certificate) for non-commercial flying done for a maximum of 28 days per calendar year. Personally I would follow through with the change of state of licence issue.