I spent half of a day working on this and I’m still not happy with it. This is what I started with.
I ended up taking this apart. It had wrinkles inside. 
Ugh. And this is why you can’t trust the accuracy of the lines on these.
I pulled out the draw string and sewed ties in.
I tied these under the table top.
Not pretty, but so far it’s okay. I’m hoping it will flatten out over time.
Have a good day!
KatyQuilts 
How fun to have a whole new empty sewing room to clutter up I mean artfully arrange! Maybe you could get one of those wool horse saddle pad things for your ironing table?
I need to replace my pressing cover; it is so stained and also ripping – LOL. I wonder if you could find a way to use bungee cords to stretch the length of the board, making the top a bit more taut? Don’t know if that makes sense, sorry – LOL
Hi Katy! It will definitely flatten out and sooner than later. You’ll be encouraging it to with the nice hot iron! I’ve never had an ironing board cover with lines, etc. I usually go for pretty. HAHA! ~smile~ Roseanne
Looks like every day you are making good progress in your new sewing room!