The Aegir documentation states that root access is required for
installation, but I have seen comments suggesting it is possible to
instal without root. If this is correct can anyone point me in the
right direction?
In addition to the installation and configuration of web and database servers, the standard installation of Aegir requires the creation of a user account and the deployment of one or more sudoers
files.
While I'm sure there are creative ways to work around some of this, each step down that path gets you further and further from a standard setup. The more bespoke your deployment becomes the more time and effort will be required to ensure its security and reliability.
I highly recommend against pursing this path.
I host a few non profit sites with an Aegir service provider who has
provided great service. But the sites have grown and the cost has
become a challenge for them.
Have you offered to cover the costs for your current Aegir service provider to scale up their hardware, move your sites to a dedicated server, etc.? This is likely to be the most cost-effective approach, since they're presumably already tooled up for the deployment and management of Aegir servers.