Good day,
I am an expert in elearning with over 17 years of experience. I have experience on many LMS's including but not limited to the ones you listed.
I'd suggest either Moodle or Blackboard; Moodle is a free open source, while Blackboard is not, Blackboard is the best ever LMS available in terms of security, functionality, usage, features and other areas. So if your budget could handle Blackboard, I'd strongly suggest it.
Although Blackboard could run on Linux systems, it is preferred to run on Windows based servers which gives it power and security.
This is not a bid, but a way to communicate with you, I need to discuss some details before providing an accurate and competitive bid.
Either system that you will choose, I will provide the feature set necessary for you.
Kindly initiate a chat with me to discuss in details.
Regards,