An update:

I've looked into this a little more, and I think the problem really is the platen and how I've re-inserted it into the machine. Right now it looks like this:



As you can see, there is a small strip of metal between the gear and the rubber itself. I don't think it should be there, and it should be a tight fit. You can't tell on the picture, but when you turn the platen, you see that the gear is pivoted slightly.

When I look at the gear that goes into the platen, I don't see any other way of putting it together that makes sense, but it won't stay stuck inside the platen, but keeps getting pushed out.

What it looks like:


How I think the individual pieces fit together:



And how it looks before I put the platen into the machine (notice how the gear is being pushed out, rather than staying close to the platen, there is a little room in which you can push the gear back inside):

Pushed in:


and without pushing:



Any idea on how you can force this gear to stay inside the platen? I believe the reason it can be pushed out is to allow you to freely adjust the platen position, without using the lever to switch off line spacer.

I've had a look at all of my SM2s to SM4s and all show the same space of metal core between the toothed wheel and the rubber - though it varies a little; from about 1.5mm to 2.5mm.  What IS different, however, is that all of mine show no gap whatever between the left face of the toothed wheel and the actual notched end of the line-space lever itself.  Your picture does show a slight gap there, I believe.
I think that your toothed wheel needs to be turned on its own centre until it seats better with the parts to its left - which means that the entire platen needs to be turned; I think this is the critical point when reinserting the platen: turn it until this gap disappears and the parts are as snug as they can be.  Hope this helps.

Magic!