How to feed Blackbirds and not Grey Squirrels?

I am out of ideas and hoping someone here can help. I have a ground feeder tray + cage which is visited by blackbirds, song thrushes, house sparrows, dunnocks and robins. Crows, magpies and pigeons are successfully kept out. But there are two grey squirrels which are taking most of the food I put out, the birds are barely getting any lately.

I've tried the adjustable RSPB cage, but if I reduce the hole size the blackbirds look at it perplexed and no longer enter, whilst the squirrels run straight in still. I have a theory urban grey squirrels have evolved to be skinnier to access feeders! So control by bird/animal size is not working.

I've also tried mixing hot chili pepper in with the food, that didn't put them off at all.

How high off the ground will ground feeding birds go for food? It sounds oxymoronic but an "off the ground" caged table in the middle of the lawn that the squirrels can't jump or climb on might be the only way to feed ground birds.

Does anyone know of any purchasable or DIY solutions please?

3 pairs of blackbirds in Nottingham would appreciate any suggestions you have!