Start from the official list
Only providers on the Ministry's accredited list can act as your ASP. The Ministry also publishes pre-approved providers still finishing accreditation. Shortlist from those lists, not from advertising, and record each provider's accreditation number in your file.
Accounting software vendors are a separate category. HelloBooks, for instance, keeps the invoice data a provider needs but does not appear on the list and does not transmit e-invoices.