Here's a video that's close: http://www.youtube.com/watch?v=ShpsREtzxrE
She uses glue and a strip of steam a seam to join the new batting.

Use coordinating fabrics
 

Just cut off the binding and add coordinating borders to the size you want using a quilt as you go method. Then bind using the coordinating fabric. Not so hard.
Or - after cutting off the binding - sew on the extra borders similar to a reverse facing. Machine sew to the back, add batting, face with the front coordinating fabric, hand sew on the front and then quilt. Again not difficult.
Well, I was going to show you one I enlarged for my DGD. She didn't want to give up her baby comforter... still has it even though she's nearly a teen! Here's hoping she doesn't want it made larger again!

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Here's a pic of the quilt I'm talking about. Because I set the blocks on point, I'm still wrestling with how to go about enlarging this quilt.

Ideally, I want to add another row of blocks all around, then another border.

That sounds like a super idea. You can "rip" the binding off (lots of work) or you can use your ruler and cutter and just cut it off. Then proceed as others have told you to put on the new blocks and borders.