I have done this kind of project before for many clients that I support. I have used CUCME as the Call Processing System integrated with Cisco Unity Express (CUE). For this project, I will use the Auto Attendant (AA) feature of the Cisco Unity Express in order to achieve the following.
1. During Business Hours (based on provided days and time), I will play the General Welcome Prompt to the caller and inform them that their call will be transfer to the next available representative. The initial call will come from the CME onto CUE IVR and then will be routed back to the CME into a Hunt Group using various algorithm such as Longest Available Representative, etc.
2. The second menu prompt will be configured to redirect the call to the on call Engineer. I will build a single scrip that will achieves both Options 1, 2 and 3. For Option 1, the call will redirected to the on call Engineer cellular phone for example. To make life easy for you, I will make sure that the script that I build for you allow you to connect on the CUE web page and simply populate the On Call Engineer Number field and click on Save and thats all.
3. Options 3 will be configured to let the customer leave a voice mail. Based on your request, the voice mail can be left to a specific voice mailbox or General Delivery Mailbox (GDM) which all representative can access, etc.