有現在完成式的問題想問問?

"contact" may not match "負責聯絡" that you may have in mind to the full extend.
"contact" 通常是用來表示"主動向外在物理層次的接觸"
若是你的聯絡是"雙向的"或是有更高層次的服務,則建議你用:

I have been reaching out to the homeless community since 2003.
I have been servicing the homeless community for the last 13 years.
I have been the point of contact for homeless community at Taipei city government since the establishment of the department.

I have been responsible for the services for and the communication with homeless community for the last 13 years.

全對。