The hardest part of it is balancing it. Do you make it so anyone can have a high chance of successfully hqing the recipe? Then there's no point for cross class skills. Do you make it so having access to the cross class skills AND the specialist stuff is not overpowered? Then the people without the cross class skills suffer for it.

My opinion is that the specialist system should give the skills, and the cross class skills would act as a small boost for it, maybe along the lines of 5-10% more for the skills. You'd still have access to the cross class skills on non-specialists, but specialists with the skills would just get the upgrade for slotting it in as a cross class skill. Specialists without the cross class skills would simply get the normal version of the skill.