The first thing you have to learn about AX is that nothing is free.
Want to use all the physical memory on your unit? That'll be a license upgrade.
Want to have the unit reachable via a web browser? That'll be a license upgrade.
Want to be able to make changes via a web browser? That'll be a license upgrade.
Want to make your four year old system work with the latest java release? That'll be a license upgrade.
My point being that you will get dinged for anything and everything. To get the software, you typically have to pay an annual fee typically in the range of $2-3k. Do you know if your JACE has an open license? If so you can use any brand of AX. There may be other options out there on how to get a copy, but everyone I know seems to be in that position. If you get someone to load a station onto the JACE for you and it has the appropriate licenses, you can do most of you work from the web browser.
Unless you are working with students who will be full time control technicians, I wouldn't focus on the fine details of AX as they are constantly in flux and the successor to AX is about to be released. Getting your students to understand concepts like MAC addresses, neuron IDs, the logic gates is a good place to start. I'm not familiar with what Trane programming looks like, but I'd also recommend getting a Distech or some other brand that has free configuration tools off ebay. Old controllers can be had for relatively inexpensively.