It's contribute, but the issue is how quest relates to the other parts of the sentence.
{My attention to sprinkle placement and sandwich-building artistry} and {my quest for the ultimate toast} consistently contribute to satisfied clients and business success.
You need to repeat my because quest is too far from the first one and it's difficult to relate the two together; a quest is also rather too different from attention to be included in a single thought — you can't have "My attention to quest". Once that has been done, the two things which contribute are the two phrases {in braces} in my version.
The sentence would be said with commas after artistry and toast, in order to make sense of the several ands. I don't believe that that phrase is actually a parenthetical insertion though, because it's not simply additional information you could leave out; it's actually part of the subject of the verb contribute. The additional my helps to separate the two elements of the verb subject.
I'm sure there are those who are more au fait with the terminology of syntax and grammar who would be able to offer a more technical analysis.