ULA is definitely not like SpaceX and is not a competitor at this point. ULA is failing due to the exact problems that you describe and if your rocket is not reusable, it cannot compete outside government launches at this point. The only other rocket company that I see competing at the moment is Jeff Bezos' Blue Origin (and we are still waiting for the first New Glen launch). SpaceX is different with Elon Musk leading the engineering. Move fast, iterate, everyone working on the project should understand the whole vehicle so that people can see when making radical changes is the way forward. SpaceX was building carbon fiber pieces for their next rocket after the Falcon 9/Heavy, and completely scrapped that idea and went with a steel hull instead. About a year later the new design is going to launch up to 15km and land in the next few weeks.
Elon Musk comes from the start-up world and he is hoping to get to Mars himself, so he is in a hurry. I would say if you can get a job there, you should. If you have not already, check out reddit/r/spacex for lots of interesting stuff about the company and what they are doing. You might want to apply to work there if you are looking for a fast paced aerospace company.
There is also the startup called Boom that is working on building a supersonic passenger plane. They have just finished a smaller human-piloted supersonic test plane to prove out their ideas and hope to have the commercial airplane in service by 2025.
These companies are both run by people that started in software and then moved to aerospace without any other real prior experience in the field. Maybe you can have a similar route with founding a successful software company and then, with that success, found an aerospace one of your own. Good luck.