I think I've been told that already... this is the point where I live up to my chosen username and realise that the actual problem is not the same as the apparent problem here. The actual problems are:
a) Having googled quilt wadding instead of making it up as I went along like we did back in the 00's before the internet took over, I have realised that my previous quilts are held together by a mixture of optimism, geometry and shite polyester batting, and that if I want to make a proper quilt it is going to involve a lot more sewing.
b) This means that if I do this properly there is absolutely no way it will be ready in time for my friend's wedding.
c) Having experienced the heavy wool quilt and the stiff polyester quilt that are shoved in cupboards, and the fluffy polyester quilt that is constantly in use, I am instinctively aware that batting is really important but having never experienced the fancier varieties I have not the foggiest idea what they are actually like.
The solutions:
1) Quilt this properly, using the method suggested by JanieW where I quilt the hearts into just the batting and backing first and then the SITD squares through the whole thing. Then I just need to make sure I get something with a maximum sewing distance of at least 4" (my square size) and labelled as "machine washable" "suitable for hand sewing" and it should be fine! (Oh drat, it looks like the ones that are best for hand sewing are wool... but I've had an entire felt dragon turn to powder before and can't face that again. And the ones I had my eye on (warm and natural and heirloom 100% cotton) are apparently rather stiff to sew by hand. Hmm). I wonder if I could get away with quilting the back, then washing it so it goes a bit crinkly, then quilting on the front after it's shrunk so the squares stand out less?
2) Accept that the quilt won't be finished by the wedding, but that I will probably be able to get it to at or near the stage I thought was finished, so I can give it half-finished so they can see what it's like and explain that I'll need another month or so to sew the squares in (and add the binding, which presumably comes after that).
3) Go to a real-life fabric shop and poke stuff to see what feels right.
Does that sound like a plan? Thanks everyone!