Does a cover exist for a 3.5 inch round electrical box?
Your problem is your supplier

There shouldn't be any trouble getting the cover you require.  However it's a rarely requested item, so Home Depot's central office has determined it's not worth the shelf space to stock.  You can take your chances with other big-box or hardware stores, but any competent electrical supply house has about a 90% chance of stocking it, having you out the door in 3 minutes, and be cheaper to boot.  (Home Depot charges gotcha pricing on anything that isn't a hot commodity). 

Also you have 8 hots and neutrals splicing up here. All grounds together count as one wire. 14 AWG wire requires 2.00 cubic inches per "wire", so you need 18.0 cubic inches.  Make sure the box is at least that large (it should say on the inside) - if not, look for a 3.5" box extension to get you some more cubic inches. You'll definitely need an electrical supply for that! 

If all else fails, put a pull-chain lamp socket there and don't use it for anything, but that will need 4 more cubic inches.