With hyperturbos the blinds go up every half orbit. Thus should I be using the NE push shove solution for the next blind level rather than the current blind level?

When I follow the normal NE recommendations, seems like I'm prone to blinding out and losing all fold equity and thus my jamming requirements probably should be quite a bit wider.

In some spots yes, in some spots vice versa. Hard to give examples as you dont have any specific situation exaplained.
One example i can come up with asap is jamming 10bb on button with 5 players left and 2 itm, is when blinds are weaker players who dont call close to correct.
In general you want to solve all these spots yourself to understand them better.
Hope this helps and good Luck!