I am still seeking very fat clips that might hold the layers on our dining table - it's a much thicker piece of wood that a 'normal' table

@LeilaMay Try searching for "Spring Clamps" on Amazon (other online retailers etc ...) as these are meant for DIY use and are larger than the plant clips I use.

This foot is for category A machines (see link below) - these have a front loading bobbin and include “badged” machines for John Lewis, Dunelm and SMD.
https://www.sewessential.co.uk/amfilerating/file/download/file_id/6132/

This what what WW2 children are expected to wear in Cambridgeshire schools 
http://www.cees.org.uk/evacuees_dress.htm

Does anyone use a paste table or similar and clips, doing it in sections? I've seen it like that on youtube and think it might be my solution in the long term?

The quilts I make are often longer than my table so as long as I can fit the width of the quilt on the table, I often use clips and pin in sections. I clip the first part of the layers to the table and pin that section. I then unclip that section, roll up the unpinned section and move the whole thing up the table so that about 6" of the pinned section is at the top of the table. I then clip the pinned section and unroll the rest, smoothing the layers as needed, before clipping and pinning that section. I repeat this until I run out of quilt to pin.

I have a large piece of thin mdf that over hangs the edge of the table and I use clothes pegs to clip the layers to this. For smaller quilts (or if I can't be bothered to get out the mdf) I put a cutting board on the table (to protect it from pins) and use the larger size of plant clips to hold the layers to the table.

I think some you tube options show the quilt layers being rolled around pool noodles or pieces of wood to make it easier to move them but my quilts haven't been big enough to need that.

I've had a quick look at coasters on the John Lewis website and they seem to be about 4x4" or a little bigger. Perhaps a mug rug could be twice the size of a coaster - half the space for the mug and half the space for biscuits.

John Lewis also had some round coasters 

(By the way, I've decided I'm in on this swap and happy to post internationally.)

 

Could be a mug rug or place mat (or set of MR's /PM's) if you want ...

I'm not sure about joining in with this - I'd feel terrible if I'd sent someone a coaster/mug rug but got a set of place mats in return.

There's a video on YouTube showing how to machine stitch hexagons and triangles which might be of interest. The hexagons are just cut from a single fabric (not pieced as in your pattern) but the method will be the same.