Not sure about Expert Flyer but even using the Avios website and (painfully) going day by day, months and months in advance, there is very little.
The pecking order for upgrades seems to be:
- Paid upgrades for cash ("bid to upgrade", only offered if booking direct with EI)
- Concierge free upgrades (four per member per annum)
- Platinum free upgrade (one per member per annum)
- Upgrades for points
- Business class award redemptions using points.
So in my view they keep incrediblyfew slots available for straight business class award redemptions as they know/assume that the various other categories will use up the space available.
It's not true that there is literally no availability for business class redemptions to the US, but there are very, very few, even months in advance.