Google's speech recognition is supposed to be much better, though not sure if they'd allow "one intent to rule them all" like you want.
For free-form speech recognition in Alexa, the best option I've seen mentioned on the public Alexa Slack team is using the "SearchQuery" slot. So you'd still have to make a weird catch-all intent that would eat up some of the words (and you wouldn't be able to see them). At the same time, you shouldn't assume that Alexa will give you very good results with such loose constraints. Even in my simple skill it's very bad about confusing certain pairs of words.
For free-form speech recognition in Alexa, the best option I've seen mentioned on the public Alexa Slack team is using the "SearchQuery" slot. So you'd still have to make a weird catch-all intent that would eat up some of the words (and you wouldn't be able to see them). At the same time, you shouldn't assume that Alexa will give you very good results with such loose constraints. Even in my simple skill it's very bad about confusing certain pairs of words.