Are there any enzymes that force one or more of their substrates to travel a relatively long distance through a small opening/tube through the enzyme and to the active site? (not a transport protein)
First of all, as you mentioned, there are a lot of membrane / transport proteins with very nice, well defined tunnels. But you're looking for a soluble / cytosolic enzyme.
Then there are some enzyme with just deep active sites, I think the p450 BM3 is quite known for that, but any enzyme with a reasonable specificity (and especially those that have very reactive cofactors) will have a "tunnel".
You can also find long "tunnels" in enzymes that accept long substrates. I like this example of squalene synthase: http://science.sciencemag.org/content/277/5333/1811.full. The substrate first has to go deep into the enzyme to find the proton it needs to start a quite interesting reaction.
If you want to find new tunnels in your enzyme there are also tools available, such as CAVER: http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002708 If you look at the papers citing this tool you might also find some cavities.