Just looking through your criteria list, I think you are in the right place.
I always like to think of SuiteCRM, not just as a CRM, but a very flexible piece of web-based software that can be configured into many other applications. Essentially, individual modules that can be developed within the software and then linked together, into a framework.
Knowing whether something is right for your application is almost impossible for someone else to determine, as there are too many factors involved. Any kind of CRM migration takes effort, but Suite provides a lot of customizable functionality to fit an organization’s individual needs.
I would strongly recommend that you either check out the online demo or download a copy to your own server and just get stuck in!
I’m sure you are still researching online. SuiteCRM was actually a fork of SugarCRM, so a lot of what you may read on the Sugar support sites are still also applicable to Suite.
The most complex item on your list is the computer-telephony integration and that is not something built into Suite directly, BUT has been done by others and is available as a paid add-on.
I would also like to add … unless you are brimming with skilled support people, don’t be afraid of external hosting providers. (I know your data is sensitive, but so is most other organization’s data). Hosting is not expensive today and you can save yourself a lot of headaches by having essentially a dedicated 365/24/7 support team to ensure that your site is up and running and kept updated with the latest versions of PHP, MySQL, etc. It becomes just one less thing to worry about!
Depending on your inter-communication requirements with other software, there are a couple of ways to do this … either a simple export/import (which can become tiresome) or by using Suite’s “logic hooks”, whereby the discrete systems can transfer data (i.e. “talk to each other”), directly. You would obviously want to look very carefully at your other software in this mix, to determine what is going to “drive” things.