You Won't Find Everything You Need in One Product
By now you may realize that you aren't going to find one product that matches your requirements exactly. You might ask yourself: If a reasonable selection of products provide most of what we need, why can't we get the functionality that perfectly matches our requirements?
The short answer is that software packages are off the rack, not custom-tailored. A good software vendor does market research, conducts usability tests, and spends years trying to develop code that makes life better for those doing certain tasks. But even the best software isn't going to meet every requirement. You have to sacrifice the dream of ultimate functionality for incremental improvement. As long as you know that the new software will deliver improvements that justify its cost, buying the product is nearly always better than writing a custom application or deciding against the purchase.
Once you are a licensed customer for the software you've selected, you should have a direct channel through which you can communicate your requirements to the vendor. In the best-case scenario, features that meet important requirements will be included in future versions of the software.
Remember to present the requirements analysis as soon as you've finished it. Strike while the iron is hot!