DIY Rig Questions (Not Exactly a Handyman)

Hi All.  I have a Medium BGE and wanted to create a DIY rig so I can do raised direct cooking (among other things).  My plan was to do it via carriage bolts and let the porcelain grid that came with the Egg rest on top of the cast iron grid that I have.  I put it together using 4 inch, 5/16 - 18TPI carriage bolts with 5/16 washers and hex nuts.  It was a perfect height when sitting on the CI grid but when I moved it around, it seems as if the washers are a little too small in terms of diameter and can slide under the grid line ruining the thing.

My question is: can anybody give a recommendation for a larger washer size that'd work with that carriage bolt?  This may sound like an obvious question but I've never really purchased washers/nuts before and at my local Home Depot, unless you're a professional contractor, you can't get anybody to talk to you.  I'm just unsure about going up in washer size, and it creating an issue for the bolts/nuts I purchased.  Do I need to go up in size on everything?  Attached is the receipt from Home Depot to show what I purchased in case I described anything incorrectly (please disregard the hanging plant which was for my fiance's Mom ).  Thanks in advance for any assistance.