There is no 'lucky' w/o 'unlucky', it's a sad reality. If I want a player to be able to make a heist that's waaay above his current standing, it has to have bad consequences as well when the dice roll badly for him; all I can do is cushion the fall a bit, but hand-to-mouth existence proves a good challenge for bean-counters.
I can, however, push some of the more punishing missions to later months. Peacekeepings, Sway Govts, Secret Bases can be safely pushed back w/o hurting the 'super-lucky great heist' potential. Assaulting gunships or shrine ships with the starting crew borders on insanity, however this creates a challenge for the most hardcore players - the ceiling should always be very, very hard to get to
This approach won't save you from the predations of negative score, but will lessen the impact; a few new starting missions would help to mend it a bit further. It is important that score can be mended by research as well... which should be displayed more openly to the player.
The idea is to create an early yearning to get either Pachyderm (to gain global range, good speed and +2 troops) or Jetbike (to gain the ability to intercept, especially easy & safe civilian targets). Maybe I should add a very early-buyable ship with better range and speed than Airbus, at a cost of 1-2 troops, because airbus->pachyderm is already a quantum leap
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This will probably be an Aircar, and also there will be (later) an Airtruck, slower than Airbus with 9-10 capacity (including unique 8-9 HWP capacity for budding beastmasters and necromancers [this will be a surprise]). This will make for a choice of 3 battery-powered (very low running costs) crafts.