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Ok, let's look at the worst case prices for getting these things elsewhere:

"New" nofinite plain DMG with backlight: $90
New link cable: $5
New EMS 64M USB cartridge (even if that's not even what you're selling...) $40
Little Sound Dj license: $10 donation because you really like Johan Kotlinski
Carrying case: Erm... let's say $30 because the case is really that rad?
So, the privilege of owning stuff you have owned, $25?

Actually, I don't have a fix for this. I think I recall someone managing to look it to one of the pages by removing that capacitor and maybe adding a resistor. Can't find the info on that now, though. If I had that info (or if I'll get time to sit down and investigate the cartridge) I could give you some more advice. You could just stick the same ROM onto both the pages and be done with it. That of course only gives you one ROM, unless...

Actually, the thing with EMS cartridges (buth these 64M ones and the earlier blue 32M) is that they have multi-ROM support. (The 64M cart is really just two 32M carts with a switch.) This means you can basically fill up the memory up to 32MBit with as many ROMs you can fit. For this you need a menu ROM which will do the switching.

There are already menu ROMs available, however these don't play well with LSDj for several reasons. I'm intending to make my own menu ROM to fix these problems. When/if I get that fixed, that will probably offset the fact that you only have one page available, since you're not limited to just one ROM anymore.

4mat: The ready-made samples part is of course only for non-chip modules/non-chip samples. As Lazerbeat mentioned as an advantage, "Infinite range of sounds available."

Also, I draw my LSDj  triangles, mainly because LSDj produces a bandlimited triangle that's not stepped in 1-step increments, and also because I want my triangle to start at the bottom of the range, not middle, so I don't get that big DC offset change at the beginning.

The link port is identical to that on GBA. It's compatible with the GBC link port. (It has a slightly different shape from GBC, but that's only so Nintendo could design GBA-only plugs if they wanted. No problem!)
What SP doesn't have is a direct headphone output. You need to plug a special adapter into the combined charging port/headphone for that. Prosound is probably a PITA unless your first name is Ralph and your last name is Tyler...

Since it relies on a long camera exposure time, it can only produce still images by nature. However, nothing would stop you from painstakingly making several frames and do a stop-motion kind of thing. Of course, every frame would be aligned slightly differently in each frame, if the rod is carried in your hand, since human motion isn't perfect. You can see this as a part of the craft, and live with it.

Of course you'd need to build the thing or convince the creator to record frames for you. (I'm not the creator and I haven't built one, so I'm not of much help.)

My £0.02:

Oscillator: You can either go analog, or use a microcontroller like an Arduino for the intelligence + the oscillator.

If you go digital, you can still do the waveforms you want, but possibly with NES/chip style bit reduction for the saw/triangle. What you want to do is probably to use a passive resistor ladder DAC, which allows you to oscillators with a few bits (as in binary bits of data) with only some microcontroller outputs and a few resistors. You will still likely want to use a 'duino if you're looking to implement MIDI. And the digital method has the added advantage of being in tune at all times without trimming.

If you go analog, I recommend a design built around the XR2206, like a simplified version of the XR-VCO by Thomas Henry. It can produce sine and/or triangle in its basic configuration. I recommend just going for triangle as sine always be approximated by using a low filter setting, but otherwise you can add a switch to choose between the two. But the interesting part is the skew function. It flips half of the waveform so you first get a triangle /\/\/\ which morphs into something like /-/-/- at medium settings and finally ////// at the highest setting.

As for controlling the synth, you basically have two options if you want to keep it analog and simple. Carbon strip or a resistor voltage divider ladder with a button for each note. Carbon strip is what the Gakken syntesizer is using for example, but I'm not sure whether this can be achieved by on a DIY level. The voltage divider ladder works like this: you have a bunch of resistors in series. One end is connected to a positive reference voltage and the other end to ground. In each step you're going to have a consecutively higher voltage. Each point is connected to a switch which in turn is connected to the voltage control input. Simple example:

       ___          ___          ___          ___          ___         
+5V - |___| - o -  |___| - o -  |___| - o -  |___| - o -  |___| - Ground
              | 4 V        | 3 V        | 2 V        | 1 V

That way you get a number of evenly spaced voltage reference points that can be used as control voltages. This system fails as soon as you press two keys simultaneously, but hey you can't get everything...

A creative way to this approach is to use a printed circuit board where you use copper shapes as keys and play the thing with a "pen" attached with a wire. This is the approach Cheap, Fat and Open is using, even though it's using a different wiring of the electronics since it's a digital synth.

A nice trick you can use to almost detune the oscillator is a sawtooth phase shifter. There's a schematic for a really simple one here: http://rubidium.dyndns.org/~magnus/synths/schematics/ I think that one flipped the + and - of one of the opamps, however.
Here's a demonstration of this effect unit in my modular homebuilt modular system, with an oscilloscope view and annotations explaining what I'm twiddling with. Vhen modulated with an LFO, it fattens up the sound a bit compared to a simple sawtooth.

As for a sequencer, what are you hoping it will control? Pitch? Other parameters? Make sure this isn't shooting over the target and that it will actually be useful.

And then there's the envelope, VCA, filter and LFO design aspects. I don't really have time to write more about this right now, and I also have less useful advice on those parts of the synth. But before I conclude, let me warn you of feature creep, i.e. adding too much shit and not being able to finish the synth, especially if you're on a deadline, which you probably are since it's a course. With complexity, the number of things that can go wrong increases exponentially. I'm of the opinion that having to debug your stuff is the best, if not the only way to gain practical knowledge. However, respect deadlines and know your limits.