My question is basically given in the title: Are there any references for a generalization of algebraic Ktheory to the scenario where the domain of the functors consists of commutative semirings (provided this has been done at all)?

There are a few papers out there dealing with a slightly different focus  algebraic Ktheory over the "field with one element" $\mathbb{F}_1$. Some of the frameworks for $\mathbb{F}_1$ algebra include semirings, so these papers might contain material that covers what you are interested in as well. The thesis of Nicolai Durov arXiv:0704.2030 describes a setting for algebraic geometry over a class of objects more general than rings. These objects are commutative algebraic theories. Commutative rings, commutative semirings and commutative monoids all form full subcategories of commutative algebraic theories. Among the many things Durov does in his thesis, he includes some discussion of algebraic Ktheory in the final chapter. The "blueprints" of Oliver Lorscheid (arxiv.org/1103.1745 and its sequels) also contain semirings as a full subcategory. According to the abstract, he will eventually get to Ktheory of blueprints, which will contain Ktheory of semirings as a special case. 

