Without seeing a copy of the score, the only thing that makes sense is to rely on the pedal to retain the whole notes. Could you possibly post a copy of just the problem measure?
big bvsc fan i have the score and cd album. this style of music is highly improvisatory in nature, the HL book is a skeleton guide and should be taken as the be all end all of the pieces. that said you'll need to some quick finger work if you insist on holding those inner notes, id probably do a rh 5 3 5 4 5 4 53 if that doesn't work i'd just play around to find what's comfortable. fingering is highly personal so your approach may be diferent. it's a slowish tempo so shifting rh 5 should be fine