I have a web server with several applications running on different ports (some on apache and some on tomcat). Clients are having difficulty at restricted sites with getting the ports open to use our applications. So I have been asked to somehow route all the traffic through the https port (443 I think).

This should be possible because all the paths for the different applications are different, as well as the different ports.

So for example I have

https://blah.com:8000/cs

which we would like to be routed as

https://blah.com/cs

but still use the original server setups to keep things modular.

I am having a general failure of google-fu when it comes to implementing because I don't know the right buzz words for what I am trying to do.

I have looked most at proxies (apache and squid specifically), but they don't seem to be designed to do this exactly, unless I am not understanding what I am reading which is quite possible.

Thanks for any help you can give!

I'd say you are looking for a reverse proxy. Apache it self has a module for it. Check out http://httpd.apache.org/docs/2.2/mod/mod_proxy.html. I'm not quite sure if this will do the trick but should give a good amount of possibilities.

I found this document on apache reverse proxies that was very informative:
http://www.apachetutor.org/admin/reverseproxies

I am still unclear about how to get apache to proxy for https. There seems to be some vague indications that it cant?

Found a package called "pound" that seems like it may be able to do what I want.
http://www.apsis.ch/pound/index_html

It also does load balancing and some other things. Doesn't do caching, though I don't care about that much since the apps I am trying to hide are all script based. So no big benefit to caching it.

looks like a nice one.

Taken straight form the apache doc:
I never done anything like that so can't realy help you. But i think your on a good way...