Why is Disney spending so much money to change the theme of a beloved ride solely in response to a twenty thousand signature petition?
Because they are not, your post outlines the absurdity of this "narrative" that Disney caved.
They have clearly been brainstorming and working on plans to change out Splash for some time, it was inevitable. Bob Iger has spoken out about SotS and not releasing it, did we really think this wasn't going to have an IP change? If so, that's just naivety at its finest (not saying you are naive, just in general).
Disney has no history of taking petitions into account, except maybe the Save Disney movement back in 2003/2004.
Splash Mountain had the writing on the wall, and Disney KNEW it would cause major push back. I assume they would have normally waited until most the planning was done so they could just announce and get going ASAP (Like Guardians Tower), but with the movement happening right now, it presented an opportune moment to announce. People can be angry, but the media will mostly favor the change/story, as will everyone protesting and marching. It comes across as good corporate citizenship. They may have had several variations of plan in the blue sky stage, and saw the current momentum, which made PatF the #1 choice. We won't ever know.
But this wasn't due to a petition.
And reminder, apart from Disney boards/fan accounts, most the Social Media chatter I find praise the change. And TBH, other Disney or Theme Park boards I look at are far more favorable of this change then the WDWMagic crowd.