A an old wool blanket folded to a reasonable thickness & cut to roughly shape can work wonders on any ironing board. They can be found at op shops at times (don’t use the acrylic as they will melt and stick). Cover with a calico cover to avoid wool fibres on whites. To attach just sew on some ribbon or decent string to use as ties under the board.
The only thing you might replace on the cover will only generally ever be the calico cover unless you leave an iron for a very long time on full heat on the board.
If you wanted to get extra fancy you could stitch elastic to the edge to act as the retainer or use a drawstring to pull it tight under the board.
Another thing we have used is a pine slab cut to shape to fit the board and glued in place (normally contact type glue), I would think plywood would do a similar job. Then just cover with a normal cover to finish the effect or you could sand and bring to a high finish as a raw board if you desired.
Learnt these from my maternal Grandmother (a household wonder of ingenuity) and Grandfather (he was an old style builder/carpenter). They grew up just before and married during the Great Depression when nothing was allowed to go to waste.