NExT is your best bet, alternatively just the xEM. (NExT is your best bang for your buck)
I’m trying to find some more Specification on your lock to confirm compatiblity… DT chose the Atmel ATA5577 chip so at 125kHz there is a better than average chance it will work.
Re, the enrolling/cloning you have a few options.
My opinion In order of ease/cost:-
**Ask you apartment manager to enroll your implant
**Use the free HID Proxalator mentioned on the link you provided???
**Buy a Blue chinese cloner (search on these forums, there is a lot of info on here) DT no longer sell them due to reliability, but on the store page there is some very good info about them. (Cheap but has some issues.)
**Buy a Proxmark from DT; expensive, not user friendly but it is reliable and has multiple uses.
** buy a CRP2 Enroller (very expensive for a single use/single purpose) Also likely to be the equipment your building manager will use
Hopefully that is enough information to get you started.
Just ask if you need some more assistance.
Let us know if you have success