Hi there! You have the same machine as me, and mine was almost as filthy. I managed to clean mine up without taking the platen out. I used a can of compressed air, and took it outside. To clean the platen, I first used a damp rag, then some Cif cleaning cream - I think your equivalent would be something called Soft scrub? I did the platen in small sections, wiping dry before moving on to the next part. I used a thin piece of plastic packaging from a cake box around the platen while using the cream cleaner to stop drips going through to the underneath. I also fed a lot of pieces of A4 paper through to work out the filth. I didn't immerse the machine in anything at all to clean the rust off. I did it all by hand with a rag and small amounts of metal polish and some very used-up kitchen scrubbers, the kind with a sort of green plastic scrubber on the top of a sponge. This gave just the right degree of scrub without being nastily abrasive on the chrome. I tried very fine wire wool, but this just shed bits of wires everywhere, and I stopped, not wanting to clog the machine up with extra stuff. It took me a whole weekend of polishing to get the thing looking decent, but it can be done. For the keytops chrome, I made some tiny scrubbing tools using a barbecue bamboo stick and a bit of old scrubber held on with a rubber band.
The mechinsm for lifting the typebars was really stiff to begin with, and I found that I had to pull out the little knob on the side a bit to lift it up and over the curve.
The drawband was not too difficult to replace with 50lb fishing line. There's a really good description of how to go about that here on this site. But I followed these instructions http://typewriterheaven.blogspot.co.uk/2012/01/rr1-carriage-strapped.html
On the remington portable you don't need to double back up over the small line guide.
I'll be posting some pictures of before and after of my clean-up on my Remington Portable 2 soon. And I'l put in a photo of the drawban

This looks exactly like the drawband fix I did on my remington portable no.2. I threaded the fishing line through first of all, then wound the mainspring etc. The mystery lever is used to lessen the tension on the mainspring, bit by bit with each tweak. You can also increase the tension on the mainspring a little at a time by using a screwdriver in the main, biggest slot there, and turning clockwise. I didn't have mine wound quite enough when I did my replacement with the fishing line, and I gave it about half a turn more - very carefully! I didnt 't want to end up having to fix the spring itself. Great pictures, and explanation very clear and thorough.

hi Uwe and thank you! I will have to get to grips with posting photos, but I'll show you what I've been up to in due course

Hello, I'm Martha, based most of the time in East Anglia. I've used typewriters since 1988 when I was given a half-dressed Silver Reed to write college essays on. It was my faithful companion wherever I went, never going wrong no matter what I did to it, no matter how I transported it... fast forward to here, and I have a few more typewriters and a lot more respect for their mechanisms much of which still baffles me.
I don't have a lot of space, so I've stuck to portables. An Olympia Splendid 66; Lettera 22; Adler Tippa 1; and a Tippa S with script type. I have a Remington portable no.2 which I bought purely as a rescue, but managed to fix it up. Those are my working typewriters for the time being. 
I'm a writer, so when I'm not pootling about with metal polish I'm using these machines pretty much every day for first drafts and for other projects, letters or whatever.
I'm really glad to have found this forum, I'm not sure I'll be able to contribute much in the way of advice, but I have enthusiasm for typewriters in spades.
cheers!