I use the same process, though I realized that to do that effectively you need to have appropriate vocabulary. An occasional press release you stumble upon, or a dystopian sci-fi movie/novel you read, serve as good sources of useful phrases.
Political press releases are fantastic for this. "If by whiskey" has become infamous, but the actual technique can still be made quite subtle. Similarly, "neither confirm nor deny" is a trope, but it was originally a lesson in avoiding giving away negative information.
Well i read a _lot_. Like during 10 years i read one book per day or more. I am lower now, but i am slowly getting back to it. So i think i have the vocabulary anyway. It is deeply engrained into me now.
I think business speak is like a second language in that I may need to switch to using it for a while and certain constructs I'll get tripped up on and others not so much. But like any language, if you use it often enough you may start to actually think using the language.
In general, i begin with "what i want to say" and then i generate the smoothest way to explain it in a sentence, without anything that someone could "grasp" on.
It tends to be enough. So i don't think i ever think in corporate speak. I just try to use my imagination.