Let's look at how much you will save if you overpay your mortgage.
€2k a month for 24 months is €48k
You will have €48k off your mortgage for an average of 12 months.
So, if you are paying 4% interest, you will save about €2k in interest over the two years.
It seems a small price to pay for the flexibility of having €48k cash.
As Monbretia has pointed out, the market may be very different in two years. They may not be doing top ups and you might have to borrow the €100k from a Credit Union or other expensive lender.
There is no harm in switching, but I don't think you should switch twice and look for the top-up from the third lender.
Switch to EBS. Stay with them until the top-up is complete and then switch to AIB.
Brendan