By cutting off do you mean that it correctly rounds towards zero? Maybe you can implement rounding to closest by just doing the calculation in a one digit wider mantissa with rounding to zero and observing the last digit, at least for an even base. It won't be rounding to even though, but for that a 2 digit wider mantissa is probably enough.

Rounding to nearest with an odd base doesn't seem to be as straightforwardly implementable from rounding to zero calculations at a higher precision.