Mound, I can understand why you use the 45421 here because later on when you play the repeating quintuplets throughout the song, that is the required fingering.
Yup, I use that consistently throughout and that is likely the reason I chose this fingering.
I'm not sure in general if it would be easier to target those octave jumps with the 3 or 4. Perhaps it's the size of my hand, but if I used 343, it seems there would be a bit of an awkward stretch between the 343 and the 21 whereas from 454 to 21 flows better for me.
Yes though, the lateral shift is the key..
If you have problems connecting the pentuplets (as I did) - try playing in various rhythmic configurations (dotted rhytms) as well as practicing stopping on both the C# you jumped to, as well as stopping on the D following the C#.. The entire cascading set of pentuplets should flow evenly and not sound like distinct elements.
Have fun! This is a crowd pleaser for sure

-Paul