Two more possibilities for smaller hands to try (no guarantees but worth a try);

Learn how little of your thumb is really necessary to fret the low E. Sometimes it's surprising how little is necessary.

Overdo the thumb so that the thumb frets the low E and dampens the A. Then play your fretted D,G,B, and high E strings. As long as the A string remains dampened the chord is still F and is still a movable chord. This is a solution because, even though the stretch for the thumb is further, the angle left for the three fingers isn't so hard to do accurately.