Howdy! Sorry for the very, very long delay in response.
There are indeed a total of 349 grins. 275 is the number of grins that come from single-bust glums. Combo-busting glums multiplies each glum's grin value by the number of glums combo-busted (e.g. 3 glums combo-busted makes all three of those glums give up 3 grins each). Looks like you already know this, though, but providing context on that 275 number.
Hope this helps and so glad you played this video game!!