round robin assignment to create batches then filter based on the assigned value save as a filtered view say batch 1, batch 2, run the saved views separately
will keep things clean and easy to check as well
the new companies you are finding have you cross checked to see if they do exist in the clay's database? by say using a geo + other filters rather than the description keywords filter? one reason could be that those do not exist and the problem isn't with the keywords you are using
also on a side note to build a list of law firms you can also use google maps as a source, that might provide better coverage
send table data is better than write to table in this regard but once the data is in the target table you still have to select the columns to add manually