How are we supposed to proceed regarding the VAT (which is regarded as a non-eligible cost) in countries where the VAT is not isolated on invoices?

The EU's attitude with all taxes is pragmatic, and if the amounts can not be easily established and are not shown on the invoices/documents received, the expense is eligible in full. A little common sense is however needed when interpreting this "concession", and if the costs are material or repetitive, an effort should be made to establish the amount (e.g. by requesting the information from the supplier).