I would remove the reducer and let the woodpecker have it,after all they are native.If a HOSP decides to try to use it,don't let them be successful.If you cannot monitor the box at all,I would suggest you take it down.

Do not use mylar strips before an egg is laid - it will spook other birds.

Try monofilament in the interim for HOSP. http://www.sialis.org/hosp.htm#monofilament

Downies will not nest in your box - they will use it for roosting.

or try a Gilbertson box paired with the wooden one - HOSP like it less.

Here is a link that might be useful: all about downy woodpeckers.