I'd recommend finding out the names of temporary employment agencies ("body shops") used by successful local hi-tech businesses. There are a range of these outfits, and you need to first identify the top ones. You will get so-so programmers through so-so agencies, and the top programmers from the top agencies.
They will have technical recruiters who know their talent pool personally. They typically have worked with them on multiple assignments. The recruiters know the technology sufficiently to match-up the right programmer with the right employer. This can be a very difficult thing for the average person to do, particularly without technical background. This is what a technical recruiter does all day, every day. Find one with experience!
It will be expensive (the best talent is expensive to begin with, and the agency tacks a HEFTY profit margin on top of the programmer's hourly rate) and if you are a small company or individual, you may have difficulty convincing a top firm to work for you. (If you are a bigger company, no problem.) Top agencies will cherry-pick both their talent and their employers.
I am not a technical recruiter - just a programmer who has worked through them for most of the work I have done over the past 30 years. I don't mind taking a somewhat lower rate, because of the benefit I get from working through an agency. (I've never been stiffed, they do all the negotiating, they don't waste my time - typically I am hired after a telephone interview, because the recruiter has already done the necessary pre-qualification.)
Depending on where you live, you might pay, say, $90/hour, with the agency paying the programmer $75. Some markets are lower than this, some higher, and of course there is some variability with the experience of the programmer. (OK, get up off of the floor now, and just BREATHE SLOWLY and take DEEP BREATHS!)
You can expect to pay a direct freelancer somewhere between the two rates. Good ones will know the going rates for a given market, and know that they can't charge the full rate that an agency charges, but can get a bit more than the agencies pay, so typically will split the difference.
BTW, it's considered in bad taste for both employers and employees to do an "end around" and cut the agency out. It's typically written into contracts - you are not to contact employees directly for (typically a year or two) after engaging them through an agency. I've occasionally had an agency give an employer a "release", or "buy-out", though, after doing a long contract for them.