Attn: Mike Lundy, or any other U.S. wood workers. Do you happen know where I can get 5/8in MDF? I have to cut out the long wings on these myself and Lowes and Home Depot do not have that size MDF.
How about if you got a couple of thinner pieces, glued them together, then made a new, local friend with a planer who could shave them down to your desired thickness? And / or, find a local woodworking supply / machine vendor to ask for ideas / how to make a friend to do it... if not the person you're speaking to in the store. "Hey, can you help me with this?" If that's an ignorant idea, it's because I have no idea what I'm doing with woodworking... but I know how to make friends with tools / knowledge... so maybe not so stoopid.

Maybe call Killian at Denton Woodworkers and see if he can bust out a couple of cuts, if simple enough.