We currently have a foam one.

Then replace with plastic or another foam like I mentioned above. Without a much larger budget you have no real options.

Can you get brick to blend in with the existing? Then replace the round top window as well with a rectangular one

As millwork said and please either remove the shutters since most of the windows should not have shutters anyway IMO do not try to remove that arched window you gain nothing and it will be expensive . Spend money on landscaping a much better bang for your buck

MWM advice was spot on. What you are proposing is complexity of a solution to a problem with a simpler fix.

Go back with another foam pediment and hope the birds smarten up.

The question is how long did it take for the bird damage to appear? If you will be replacing them yearly go as inexpensive as possible. Usually birds peck where there are bugs--especially when we are talking foam or other non wood materials. It's very unusual for a bird to bother with foam/plastic. Could you have a wood one crafted or possibly a plaster cast could be made to pop in there not unlike the work done around light fixtures. I see you have copper awnings...maybe something metal....

Foam or PVC because they are molded to keep the cost down.

Here is the house without shutters.

House looks more solid and substantial without the frivolous shudders.
Millworkman has the most practical and economical suggestion.
Can the foam be colored to match the window overhangs currently by the front door?

I think shutters make everyone here shudder.

I strongly dislike woodpeckers! I have a friend who has one that comes back every year and damages the same spot on his house - there are no termites/bugs. This bird made so much damage every spring/early summer (and the spot was about 7 feet over his bed - so, he'd bang on the wall - it would go away for awhile - and then come back. He really wanted to buy a BB gun and shoot it - but he didn't. Not sure how long it took for it to finally stop.

About a month ago, I was at home during they day and my dogs were freaking out because of an odd noise. It sounded like vibrations or something near my fireplace in living room. Then it stopped, and about 10 minutes later, I heard the same noise near the fireplace in my kitchen.

Apparently, male woodpeckers like to peck on shiny things to draw attention from female woodpeckers? I have this air gun that shoots salt crystals (not damaging to animals - but will scare many animals that you don't want in your yard). I shot the gun up at the three different metal chimney flues on my roof - and sure enough, a woodpecker went flying off. He hasn't come back since.

I do have these but could that not be filled with some kind of plaster then painted black