This almost sounds like you're creating a false dichotomy where fixed-fee automatically implies lower quality because there isn't a per-job incentive to do well. But, that is taking the extremely short view — as in, you're only looking as far as your current job.
What about the next job? Is your current client going to recommend you if you do a shitty job? Are you doing a shitty job if you don't write tests, documentation, etc.?
Word of mouth referrals are huge in freelancing. Your best path to success is building up a great reputation as someone who does really good work. Work that people are willing to pay a lot of money for.
Read this: https://www.kalzumeus.com/2006/08/14/you-can-probably-stand-...