Well, this is a strange one. The mandatory compensation for denied boarding is 250 Euros, so apparently less than you were offered for volunteering. That doesn't make a massive amount of sense.
However, I think you still have a claim.
This may get complicated depending on the relationship. I think it's pretty clear that BA planes are being used on the route because of the operating licence difficulties caused by Brexit. However, I'm not clear if BA have just taken over the route or are operating it as a wetlease for EI.
The former - BA are on the hook. The latter - I think it's EI as to all intents and purposes it's an EI flight. This would explain why EI have paid the duty-of-care.
Now here's where I think you should go.
If EI don't think you were voluntarily denied boarding, then presumably they must think you were involuntarily denied as you clearly weren't on the flight and did get re-booked.
Therefore EC261 Article 4 applies.
Article 4
Denied boarding
1. When an operating air carrier reasonably expects to deny boarding on a flight, it shall first call for volunteers to surrender their reservations in exchange for benefits under conditions to be agreed between the passenger concerned and the operating air carrier. Volunteers shall be assisted in accordance with Article 8, such assistance being additional to the benefits mentioned in this paragraph.
2. If an insufficient number of volunteers comes forward to allow the remaining passengers with reservations to board the flight, the operating air carrier may then deny boarding to passengers against their will.
3. If boarding is denied to passengers against their will, the operating air carrier shall immediately compensate them in accordance with Article 7 and assist them in accordance with Articles 8 and 9.
You've received the assistance in accordance with Article 9, Right to Care, albeit you can also claim the transport cost (taxi) to and from the hotel. You were also offered an alternative flight under Article 8 (there are other arguments around whether or not EI could have more here to get you away earlier, but let's not complicate it for the moment).
You are also entitled to delay compensation under Article 7, because crew shortage is operational and not extraordinary.
Article 7
Right to compensation
1. Where reference is made to this Article, passengers shall receive compensation amounting to:
(a) EUR 250 for all flights of 1500 kilometres or less;
So I would write back to EI claiming the 250 Euros.