Given the goals of the class, I think the TTL approach is fine, and I say this as an "FPGA guy". FPGAs are a sea of logic and you can do all sorts of fun stuff with them, but there's only so much that's humanly possible to do in a semester.
Looking at your syllabus, your class is a mix of the logic design and "machine structures" courses I took in undergrad. (Plus, it's for CS majors. I'm all for CS majors having to face real hardware--letting them get away with writing code seems like a step back.) At this introductory level, where you're going over how assembly instructions are broken down, I see no real benefit to having students do things in code versus by hand. Doing HDL means learning the HDL, learning how to write synthesizable HDL, and learning the IDE. This is a lot more conceptual complexity and re-abstraction. Plus you have to deal with software issues.
Generally the point of a course that uses FPGAs is to practice creating logic that is useful--useful for talking to peripherals, serial comms, RAM, video generators, etc. This is valuable knowledge to have, but it seems very much out of the scope of your course. More advanced classes in computer architecture have students implement sophisticated CPUs in FPGAs, but again, this seems out of the scope of your course.
I would at the very least devote a lecture to FPGAs. Run through a few demos with a dev board and show them the workflow. Since you're at Mills, perhaps you could contact the folks at Berkeley who run CS150/152 and go see how they do things.
I did some research and found out that there's some really simple solutions. There's a software project by the name of minimodem which allows two computers to communicate over audio signals transmitted either over a cable, or over speakers and a mic.
This minimodem project is compatible with another project Arduino RTTY (Radio TTY) which literally gives the API RTTY.tx('Hello World'), from which the data can be picked up on a PC with a soundcard.
Going in reverse (transmitting from a PC/smartphone/etc to an Arduino) is significantly less well documented.
The general concept is called (Audio) Frequency Key Shifting ((A)FSK) and there are guides from TI and other manufactures of how to do it. Most solutions attach a small daughter board to handle the ADC, however it's documented that for low bit rates, the Arduino can handle this using the on-board hardware alone.
Best Answer
Digital design does not have a lot in common with software development (maybe except that Verilog syntax looks a bit like C language but it just looks). Thus it is very hard to answer this type of question adequately. But as a guy who walked a path from software development to hardware design I'll give it a shot. Looking back at myself, here is how I would have advised myself back then if I knew what I know now:
Start from scratch
Forget everything about software development. Especially programming languages. Those principles do not apply in digital design. It probably would be easy for a guy who designed a CPU to program it in assembler or even C, but an assembler programmer won't be able to design a CPU.
On your learning path do not tend to solve what seem to be an easy problem with your existing knowledge from software. One of the classic examples is a "for loop". Even though you can write a for loop in, say, verilog — it serves a different purposes. It is mainly used for code generation. It may also be a for loop as software developers see it, but it won't be good for anything but simulation (i.e. you won't be able to program FPGA like that).
So for every task you want to tackle, don't think you know how to do it, do a research instead — check books, examples, ask more experienced people etc.
Learn hardware and HDL language
The most popular HDL languages are Verilog and VHDL. There are also vendor-specific ones like AHDL (Altera HDL). Since those languages are used to describe hardware components, they are all pretty much used to express the same thing in a similar fashions but with a different syntax.
Some people recommend learning Verilog because it looks like C. Yes, its syntax is a mix of C and Ada but it doesn't make it easy for a software developer to lean. In fact, I think it may even make it worse because there will be a temptation to write C in Verilog. That's a good recipe for having a very bad time.
Having that in mind, I'd recommend staring from the VHDL. Though Verilog is also OK as long as the above is taken into account.
One important thing to keep in mind is that you must understand what you are expressing with that language. What kind of hardware is being "described" and how it works.
For that reason, I'd recommend you get yourself some book on electronics in general and a good book like this one — HDL Chip Design (aka as a blue book).
Get a simulator
Before you start doing anything in hardware and use any Vendor-specific features etc., get yourself a simulator. I was starting with a Verilog, and used Icarus Verilog along with GTK Wave. Those are free open-source projects. Run examples you see in books, practice by designing your own circuits to get some taste of it.
Get a development board
When you feel like going forward, get a development board. If you know that your employer wants to go with Lattice, then get Lattice board.
The programming methods are very similar, but there are details that are different. For example, different tools, different options, different interfaces. Usually, if you have experience with one vendor, it is not hard to switch. But you probably want to avoid this extra learning curve.
I'd also make sure that the board comes with components that you are planning to use or is extendable. For example, if you want to do design a network device like a router, make sure the board has Ethernet PHY or it can be extended through, say, HSMC connector, etc.
Boards usually come with a good reference, user guide and design examples. Study them.
Read books
You will need to read books. In my case, I had no friends who knew digital design, and this site wasn't very helpful either because of one simple thing — I didn't even know how to phrase my question. All I could come up with was like "Uhm, guys, there is a thing dcfifo and I heard something about clock domain crossing challenges, what is it and why my design doesn't work?".
I personally started with these:
FPGA vendors have a lot of cookbooks with best practices. Study them along with reference designs. Here is one from Altera, for example.
Come back with more specific questions
While you go through your books, simulate a design, blink some LEDs on your development board, you would, most likely, have a lot of questions. Make sure you don't see an answer to those on the next page of the book or online (i.e. in the Lattice-specific forum) before asking them here.