I think, rather than combine degrees/minutes/seconds into one "number", I'd try to separate them out. This would be pretty easy with the Text to Columns command on the Data menu.

Then, you can use the =vlookup() function to return the multiple to round the seconds to. Something like =vlookup(949.393,{0,10;251,5;501,1})
Then, as you noted, use the MROUND function to get the rounding. =MROUND(17,vlookup(949.393,{0,10;251,5;501,1},2)) should return 17.

Replace the values with references to cells with those values as desired. It might also be preferable to pull the lookup table out and have it in the spreadsheet rather than hard coded into the function.

At this point, it would be easy enough to use the concatenate function to put it back into the 0° 0' 0'' format if desired.