Hey, I'm doing filters today (semi-exotic linear phase with Chebyshev stopband) and Williams' book is on my lap.
A 4th order Butterworth is down almost 40 dB at 3x Fc, so that's not a lot of filter. I'm not a digital filter jock, but I've taken a simple state-variable type analog filter design, 4 integrators in this case, and simulated that digitally in a uP, fixed-point or floating math. Works great, don't know why, and it's a lot simpler than a typical cookbook digital filter. As the sample rate/cutoff ratio increases, the integrator coefficients just get smaller.
Yeah, a FIR (transversal) filter needs a lot of taps at this high sample rate/cutoff freq ratio; you're basicly building a very long delay line. IIRs, with feedback, are better but still a bit of work.
Multiply-and-sum should be one clock on a decent DSP chip.
John