[Malsomnus]

This was bloody annoying to do... I shouldn't have neglected my math studies... but this seems to work, generally speaking, even though it's not perfect mathematically, and the code is a bit ugly as well.

function smooth_helper (a, b, weight)
   -- Assuming both a and b are in 0..359 range
   local direction = 1
   if (a-b)%360 < 180 then
      direction = -1
   end
   
   local delta = math.abs(a-b) % 360
   if delta > 180 then 
      delta = 360 - delta
   end
   
   return (a + direction * delta * weight) % 360
end
 
function round (n)
   return math.floor(n+0.5)
end
 
function smooth (tbl) 
   ret =  {}
   local avg = 0
   
   -- To make the averaging less ugly, make a padded copy of tbl
   local tmp = {tbl[1], tbl[1]}
   for i=1,#tbl do
      table.insert (tmp, tbl[i])
   end
   table.insert (tmp, tbl[#tbl])
   table.insert (tmp, tbl[#tbl])
   
   for i=3,#tbl+2 do
      avg = tmp[i]
      avg = smooth_helper (avg, tmp[i-1], 0.15)
      avg = smooth_helper (avg, tmp[i+1], 0.15)
      avg = smooth_helper (avg, tmp[i-2], 0.05)
      avg = smooth_helper (avg, tmp[i+2], 0.05)
      
      table.insert (ret, round(avg))
   end
   
   return ret
end

You can play around with the weights, naturally, and I suspect that changing the order of those smoothing lines would change the outcome in a way that would make a mathematician cringe

[Edit]
A mathematician, or someone who takes their computer graphics seriously, would have done it with vectors