The fastspi library has code for the TM1809 LED driver which uses a clockless data line as well. Two clock cycles is well within the precision possible on an arduino or PIC if you disable interrupts for the duration of the write. The fastspi library simply defines two specific counts of nop instructions to insert into each loop to make the data sending work out right.

a few possibly relevant pointers from someone else doing LED matrix code for the first time...

Have you considered that you can implement 16 brightness levels with 4 loops instead of 16, if you insert delays of different lengths into each loop?

Be sure you take branch length into account, otherwise some cycles of your loop will execute much faster than others, causing inconsistent brightness.

16 linear steps of voltage-on time does not produce 16 consistent levels of brightness.  You need a logarithmic curve to get a looks-linear response.