Hi, welcome to the forum
I'm afraid to say that your question looks like quite a headache, but you've probably already realised that!
Are the white/red/smoked components always in this order in terms of largest to smallest component, i.e. whatever random species you've got for your white fish the quantity within the mix always totals more than the random species for the red fish, and in turn the total content of those is always more than the smoked fish?
If not, then you have an extra headache, as your compound ingredients should be in descending order of weight, and if this changes, your label should change...
I'm not a fish person but the question aroused my curiosity. Your products appears to be outside the scope of Regulation (EU) 1379/2013, and the associated requirement to provide commercial and scientific name of the species, which certainly works in your favour.
I don't imagine that the "and/or" labelling option in point 7 of Part A of Annex VII of Regulation (EU) 1169/2011 would be applicable for your products, so won't help here?
However, I do think that point 5 of Part B of that same Annex could help:
Without prejudice to Article 21, ingredients which belong to one of the categories of foods listed below and are constituents of another food may be designated by the name of that category rather than the specific name.
5. All species of fish where the fish constitutes an ingredient in another food and provided that the name and presentation of such food does not refer to a specific type of fish.
This gives the designation option of "fish", so it implies that that you could group them all as "fish".
Are you specifically using front of pack / descriptive text / pictures / advertising to draw attention to the smoked / oily / white fish mix?
If so, this definitely makes it somewhat more complex, as you're then open to the question of whether those are adequate descriptions - is a consumer going to understand what they actually mean? Guidance on this seems a bit variable, and in this case I'd honestly be inclined to pick up the phone to whoever the responsible authority is (FSAI?). It's always been my experience that trying to talk to regulators proactively only results in a positive and beneficial relationship in the long term