I can read/write the HF side without Problem using my Phone and the PM3 Easy.
I want to use the LF side for Access Control, Vehicle Start, etc.
Unfortunately, I have no bigger Reader than the Proxmark3 Easy.
For a custom Ferrite Core Antenna, I found this thread:
Before going through all that trouble of Optimizing and buying the parts I need for that project, I would consider just buying the pretested Version of the RDV4 and ProxLF antenna, they should (I hope at least) work definitely.