First I wonder: what you mean exact by "in the cloud"? (hype term...)
Then: you want to click on a mail-link in Cardbox. Ok, which email client is activated then? Something in a (local!) browser or your local email program?
If I read carefully your first mail again, I understand you want to access your database from several locations. Cardbox can this easy make happen, it is standard functionality. You just need port forwarding and a little firewall configuration.
I do not recognize file/recordlocking problems in Cardbox 3. That were Cardbox 2 problems of 15 years ago or more. If you met them, there is something wrong in your configuration.
Just a thought: I think that there is a port available (perhaps 3389) for remote administration in you network. In thst case I cannot think one reason why port 3105 not can be open for Cardbox traffic. It is no problem firewall exceptions to make for several accounts in your network I think. Just keeping a list. Your IT can explain it fine (but do they want to...?). Btw: the traffic between client en server is secured.
If if you like/need after so long to change to another program: you will miss Cardbox. I am very interested what the alternative will be! Let us know!
And please tell me also why opening a port for Cardbox a messy solution would be.
Regards
Bert