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I can't imagine that millet seed would not pass through even the smallest holes?

Songbirds like it.

If you have a Wild Birds Unlimited near you, they're a great resource for fresh seed. I used to get a lot of chickadees and yellow finches at my feeders with these seeds. And they're small enough that they won't clog your feeder up.

https://order.wbu.com/shop/bird-food/bird-seed

They love it, just keep it dry, like under an eve or overhanging corner.
Don’t overfill it or it can rot if it gets wet.

Looks like it is designed for small birds so look for finch blends; you can find them online or at any store that sells pet foods.

If you have squirrels; they will destoy anything not made of metal and glass.

We use a plain old feeder that has plexiglass sides. We get a wide variety of birds. But we have to bring in the feeder at night or remove the plexiglass or raccoons will destroy the feeder.

You will have to buy smaller type seed for your feeder but you won't get the variety of birds.

I would just look for a cheap bird feeder with plexiglass sides that you can slide up or down depending on the size of the seed.

or otherwise 'modify' the damned thing? (it's not working now - what's to lose?)
In descending order (of utility and availability) a drill and bit, a file (or sandpaper), or a penknife.

And don't worry about delivering too much food/seed - because rest assured that the damned birds are going to toss it around and waste a lot of it anyway. (and usually somebody will eventually get to what goes on the ground - mostly)

...... Dremel tool and ask them to open the arches. 5-minute job if you were here. It would be fixed faster than it took me to write this post.

https://www.amazon.com/s?k=dremel+tool&crid=29R9DQLIDKUOA&sprefix=Dremel+tool%2Caps%2C131&ref=nb_sb_ss_ts-doa-p_2_11

Your local hardware store will have them. DON'T BUY ONE. I'll bet you have friends who will have one.

If they are craft people, they will likely have one.

The only problem we have with them is squirrels. It would be a pretty poor design that didn't accept a variety of feeds.

We have a goldfinch feeder that uses Nyger seed. The seeds are similar in size and shape to caraway seeds - long and thin.

The product description states "For all types of seed mix, sunflower seed and peanut bites" - note "peanut bites" not whole peanuts.

But safflower seeds should work, they are generally smaller than whole sunflower seeds. There are supposed to be two sections for different sizes of food. Sounds like the section for smaller feed needs millet and thistle (Niger) seed as others have mentioned.

I wonder if you got a product that incorrectly had both sections for smaller seed?

In any case I would definitely contact the company.

There are many places to buy better and more variety of seeds. Look for a farm supply store near you if all else fails. (google "tack and feed store near (wherever you are)" ).