I think we do everything on your list and do it really well. The only things I can see as possible issues is that we are an Australian software company, so I am not familiar with how suitable our package would be for your region.
The other point is that our software is Windows based so runs on Windows OS and not "the cloud". If you wanted remote access to your data from outside your business you would need to utilise a Microsoft technology such as Terminal Services.
Barcode printing is built in, as is batch and serial number tracing, and generation and emailing of PDF's is done in one step. The system has a very sophisticated special pricing system and is fully multi-location aware.
It also does multiple units of measure which is sometimes handy in the food distribution industry, i.e., units, cartons, cases, dozens, and does conversions between these different units and can track different pricing arrangements for different units and so on.
If you have your own vehicles for distribution than you can go with zone management, run sheets, etc., for working on what goods go on what delivery runs and so on.
The minimum components you need which covers all of the above except zone management is:
Professional Edition 5 User
Electronic Document Exchange
Stock Tracing Extensions
Pricing can be found on our website.