You may wanna look at ServiceDesk Plus MSP by ManageEngine. It is an ITIL ready IT help desk for MSPs with an intuitive user interface and robust functionalities. You have the option to choose between hosting it locally and signing-up for the Cloud version. Some of the key features that might be useful for you are:

Account management- Manage multiple client accounts, and multiple users within each account. Walled-garden approach to account management helps you secure and maintain privacy of data of each account. 
Rebranding- Personalize your login page and self-service portal so that the end-users feel like they are interacting with an internal IT help desk.
Automated billing- Promptly and accurate bill your clients for services provided.

Needless to say, ServiceDesk Plus of course comes with all the modules and functionalities of a robust IT service desk, from incident management to asset management, project management, integrations, reporting, etc. It also supports powerful automations and customizations that can boost the efficiency of your IT help desk.

Link to visit :https://www.manageengine.com/products/service-desk-msp/

ManageEngine ServiceDesk Plus - Help desk + asset management + project management . Now, avail ServiceDesk Plus On-demand for Non- IT departments with enterprise service management feature. Check out here for better clarity https://www.manageengine.com/products/service-desk/enterprise-service-desk-management.html

ManageEngine ServiceDesk Plus - Help desk + asset management + project management . Now, avail ServiceDesk Plus On-demand for Non- IT departments with enterprise service management feature. Check out here for better clarity https://www.manageengine.com/products/service-desk/enterprise-service-desk-management.html

You may wanna look at ServiceDesk Plus MSP by ManageEngine. It is an ITIL ready IT help desk for MSPs with an intuitive user interface and robust functionalities. You have the option to choose between hosting it locally and signing-up for the Cloud version. Some of the key features that might be useful for you are:

Account management- Manage multiple client accounts, and multiple users within each account. Walled-garden approach to account management helps you secure and maintain privacy of data of each account. 
Rebranding- Personalize your login page and self-service portal so that the end-users feel like they are interacting with an internal IT help desk.
Automated billing- Promptly and accurate bill your clients for services provided.

Needless to say, ServiceDesk Plus of course comes with all the modules and functionalities of a robust IT service desk, from incident management to asset management, project management, integrations, reporting, etc. It also supports powerful automations and customizations that can boost the efficiency of your IT help desk.

Link to visit :https://www.manageengine.com/products/service-desk-msp/

Coming in a little late here but ManageEngine's ServiceDesk Plus certainly matches all your requirements. You can host it locally (also offers Cloud deployment though) and it is free for your number of technicians required. It comes with an integrated, searchable knowledge base that is accessible to technicians and logged-in users and suggests resolutions based on the ticket/query. You can import end-user info, assets info, etc from .csv. It meets your other requirements as well, with powerful reporting capabilities, both out-of-the-box and custom reports can be generated and represented as graphs, charts, etc. Backing-up and exporting data is also supported. The best part is that it is not a stand alone IT help desk. It comes with native problem, change, asset, project, contract management, CMDB and other modules with powerful automations and customizations.. Over and above this it integrates with other IT applications to provide you a centralized control over all your IT operations. Definitely worth checking out.

https://www.manageengine.com/products/service-desk/

From the looks of it, you may not have a huge technician base but you do have a lot of users. A simple help desk software with automated ticketing system, workflows and self service portal will help immensely, especially to track your tickets (IT issues/complaints). ManageEngine's ServiceDesk Plus, as you've mentioned, is an ITIL based help desk software with easy automations and ticketing workflows. It converts emails to tickets automatically, so you can keep track of them and close them when you have a resolution. You can add resolutions to a knowledge base as knowledge articles for future references. This will help save time and effort spent in working on similar issues. And you can also automate ticket closure by setting up one-time rules. So it really isn't going to steal away time from your schedule.

The policy for the free edition has been changed. Each edition (standard, professional and enterprise) is free up to a limited number of technicians and nodes. You can check out this link for more information: https://www.manageengine.com/products/service-desk/free-it-help-desk-software.html