Thanks for the response Nando.
I have heard of Lucee. I haven't had any time to really look into it yet, and needed to get this new server up and running as quickly as possible. So I decided to just stick with the same versions of everything that I've been using. It's been working well enough for me so far.
I managed to partly solve my problem. In server.xml I added a new host entry for every website that I created. This appears to work, but it's an inconvenience to have to do every time I create a new site. I'd welcome any thoughts on how to get around the manual process. For others who may be stuck with a similar problem that happen across this thread:
<Host name="localhost" appBase="webapps">
<Context path="" docBase="C:\inetpub\wwwroot\" />
</Host>
unpackWARs="true" autoDeploy="true"
xmlValidation="false" xmlNamespaceAware="false">
<Context path="" docBase="d:\sites\NSC\" />
</Host>
unpackWARs="true" autoDeploy="true"
xmlValidation="false" xmlNamespaceAware="false">
<Context path="" docBase="C:\Sites\WDMTG\" />
</Host>
...and so on...