Help with Manuel de Falla pieces - fingering and voicing

[4thmg]

Hello,

I was wondering if anyone could give me some pointers for de Falla's "Four Spanish Pieces" specifically with second piece "Cubana":  I'm trying not to use the sostenuto pedal and I've figured a way to do this by using the sustain pedal in certain parts without getting things muddy in order to bring out the staccato in the bottom voice from measures 1-3, but then it gets tricky after that.  For instance, in measure 4 in the bass clef, how can I go about keeping the half notes sustained without compromising the staccato? I appreciate it.  https://imslp.org/wiki/Piezas_Espa%C3%B1olas_(Falla,_Manuel_de)