You will have to hand assemble these things with a 1K budget.
Not necessarily true. Many Chinese PCB assemblers will do this for under $1K. Use pcbshopper.com to compare prices. You'll find that assembly kind of "starts" at around $500, but given this is quite a large design, it's closer to the $1000. Note that in reality, the price will be a bit higher due to the need to buy excess components compared to hand soldering, and then there are either extra fees for sourcing, or extra shipping fees if you source the components yourself and ship them to China. That's why it gets near $1K, but it should be enough. Not much leeway though.
(I'm assuming the $1K budget is for PCB&assembly only, and doesn't include the basic component cost, because that's what you need to buy anyway, and we have no idea how expensive the components are.)
Budget is (barely) there, but IMO the decision depends more on:
* Do you have experience on producing the necessary files, instructions, and communicating with PCBA fabs? Do you want to invest your time to learn this for future projects? If no, do it yourself.
* Is there any chance this is going to be manufactured in bigger numbers (even just 10-20) later? Then buy the assembly service now.
If it's
really a one-off, and you think you're going to do similar small one-offs, similarly with limited budget (or even more limited), it's probably a better investment to get better reflow equipment and get better at it.
On the other hand, if it seems like you could have small budget increases, and in the future need to do 5-10 pcb batches with $2000 budget instead of $1000, then learn how to go the Chinese assembly route and use your precious time in design work & lower level prototyping - you are going to solder things up anyway!