I have run a campaign for several years in which alignment was subjective/optional, and found that simply removing all spells that require objective alignments to function did the trick. A couple of "protection from outsiders" spells fills in the gap by the lost protection spells, and everything runs quite smoothly.

I'm confused by your description of outsiders, however. You wrote:

Outsiders with alignment subtypes are formed from human conceptions of ‘good’ ‘evil’ ‘chaos’ and ‘law’.... They are objectively one alignment or another.... They cannot commit acts that they believe would deviate from the alignment subtype they possess.
However, in your campaign, humans don't agree on what ‘good’ ‘evil’ ‘chaos’ and ‘law’ represent. If an outsider of pure good is only barred from an evil act if he believes the act to be evil, he can do evil all day long so long as he's of the opinion that he's doing good. The trouble you're running into here stems from trying to have both subjective and objective morality living side-by-side. It is a logical paradox: if an objective morality exists, then subjective morality is merely wishful thinking or self-deception. It has no validity. Contrariwise, if all subjective moral standards are equally valid, then objective morality is a mere fiction.

Does your system need outsiders to possess alignment subtypes? Perhaps angels and demons and such could come in various different flavors of good and evil, much like people. Maybe alignment in the outer planes is just as subjective as on the material realm; outsiders are simply more obsessed about it.