I still think that flooring would be better; however, if you did insist to do this rounding instead then you could use a different convention for numbering seco

I still think that flooring would be better; however, if you did insist to do this rounding instead then you could use a different convention for numbering seconds with e.g. -30 to +30 instead of 0 to 60. However, I think that this is not worth it, and that the existing use of flooring is much better, although if you want such precision with timing then you really should display the seconds, rather than using a clock that does not display seconds, anyways.