I didn't say all tos are parts of infinitives, nor that all infinitives have tos. In your example there is no To to be part of the infinitive, but if there were, it would be, as I said.

And I'm not sure that in your example clean is in the infinitive, from my English-as-a-foreign-language classes.

I completely agree that there is no current rule against splitting the infinitive and that to boldly go is way better than either alternative, but I stick to my point that when the infinitive is in the form to verb, that to is part of that infinitive.

Gimme another hair, this one's gone to Croatia.

Split, get it? Bwa ha ha ha ha.