That looks more like psoriasis than eczema with it being red blotches in defined sections. My middle child has both and they are very different visually.
He is so bad we even get DLA for him.
You do need to moisturise loads. Keeping the skin as hydrated as possible is the only way to keep it clear and ease the pain with it's bad. You need to be applying hourly. Have you got wet wraps? That will make a huge difference. They are out on damp over a thick layer of moisturiser at night (and during the day if it's really really bad) and keeps the skin cool and allows plenty of time for the moisturiser to work. It helps stop the itch/scratch cycle too. You can get long sleeve vests, leggings, gloves, socks and even balaclavas.
What steroid have you got? That needs to be applied twice a day and wait at least 30 minutes before putting on moisturiser to allow it time to sink in. Once the area is clear you need to carry on with it for another 2-3 days to ensure it's properly cleared in the underlying layers of skin.
You won't get oral steroids for the skin. My son has asthma too and when he is on them for his asthma his skin is amazing but they won't prescribe it because the length of time required for proper treatment and dosage not suitable.
It's trial and error with moisturisers and steroids. They work for a short time then stop.
As well meaning as people are they always trot out 3 things on these threads and parents with children who have properly bad skin conditions (inpatient treatment and dermatologist diagnosis/testing etc) are fed up of hearing - aveeno, that shite lush cream and e45. None of these will work for someone with bad skin conditions. Mild to moderate maybe but not severe. As you say yourself aveeno only works when it's good. It's good for maintenance.
You need a moisturiser that is very thick and greasy. Doublebase is a good one. It's a gel so easy to apply for wriggly toddlers. We are using hydramol ointment at the moment. It's like thick Vaseline and very heavy. It works wonders though.
Keep a list of what you have tried because it's easy to forget because there are so many. Press for a proper steroid (hydrocortisone won't cut it, betnovete or eumovate would be the better options at this stage) along with a thicker moisturiser, antihistamine to help with the itching (chlorphenamine is brilliant but it is drowsy) and wraps for night time after a bath (daily bathing is ESSENTIAL when wrapping and when the skin is open to prevent infection so ignore those saying to stop bathing).
Good luck and I'm here is you need any help or advise. Even just to moan to and virtually cry on my shoulder at 2 am when you are up for the 17th time that night.