I would look into JLCPCB's PCBA service. (PCBWay and others also offer similar.)
Assuming you're not trying to do multiple spins of the same project per week and your parts are relatively common, outsourcing this to them seems entirely doable. (I only use them for hobby projects where I'm under no deadline at all, but with DHL I can get about one cycle per week.) If you're editing the PCB between revs, you're already paying almost all of that latency already.
If you can skip the "soldering by hand takes hours" step, you can get back a lot of time as you know; that might be enough to pay for the once-per-week cycle. This also gives you a very clear and fast path to go from "I had 1 unit that worked on my bench last week" to "I have 20 test units ready now" to "I can have 1000 for the Kickstarter in a month."
Last time I used their PCBA service, they had a terrible treatment of connectors, meaning I had to hand-solder those still. I understand that's improved, but not ordered in over a year.
No connection, other than satisfied customer: https://jlcpcb.com/smt-assembly