More to the point, what does "surry" mean? At it sounds as if that really is what they're singing. How you spell it I have no idea, but a number of lyric sites do seem to go for "surry" (not that I really trust lyric sites to get spellings correct).
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I agree mostly with the interpretation given of "stoned soul picnic," but I have a different interpretation of the word "soul." One could look at this phrase, as "stoned, soul, picnic;" a picnic of soul and the stoned, but also as a picnic of stoned souls; a picnic whose inhabitants are intoxicated by recreational or illegal drugs (typically cannabis sativa?).
For the definition of "surry" see the Urban Dictionary definition at https://www.urbandictionary.com/define.php?term=surry.
I'm just going to put this out there:
'Surrey is a four wheel, four person, door-less horse drawn carriage.
In this concept 'Surrey on down' certainly makes sense as take a Surrey to the picnic.
And, even 'Can you Surrey' makes some sense if you interpret it as 'Can you ride a horse drawn carriage'?
I don't know if I'm right, but this is how I always interpreted the so