I decided that my original answer works well, except for one issue.

=IF(COUNTIF(E1:H1,"?*")>=2,INDEX(E1:H1,SMALL(IF(E1 :H1<>"",COLUMN(E1:H1)-COLUMN(E1)+1),1)),"") (for the first nonblank)

gives me what I want, but it needs to return a blank if there is no text to be returned (for example, if a particular row only has 3 non-blank text cells, it needs to still work for the 4th non-blank but just return "" so it appears blank). Instead, in the cases where there isn't any text to be returned, I get a #NUM! error.

Any tips for how to get rid of this error and replace it with empty text like ""?

Thanks!