I'll leave the usual mine vs buy, ROI vs no ROI, cloud vs no cloud, SPT vs BM vs Avalon etc. aside and just tackle the subject's question and related bits:
Can you get 16NM or 20NM ASICs?
Not at this time. The only 20nm publicly claimed to have been released was used in KnCMiner's Neptune - the chip which was not available for individual sale if I recall that correctly. KnCMiner are also the only ones with a public claim to 16nm with their Solar chip, which they'd only employ in their own mining farms. I wouldn't get too hung up on the node process anyway.
I have a feeling it would be a lot more work to assemble a working rig if one were to drop a few hundred grand
You'll need somebody well versed in electronics design (digital and analog) to actually design that PCB for you. Even if you take an open source design (e.g. Avalon - SFARDS has also released detailed schematics and have a dev kit), there's little reason to think you could manufacture cheaper than the source. You'd be cutting out operational overhead, mostly.
If you did want to try sourcing chips, see:
https://bitcointalksearch.org/topic/who-are-the-manufactures-currently-selling-chips-1002697Here's a decent play-by-play of getting a chip with just enough information to get it working and designing board(s) around it:
https://bitcointalksearch.org/topic/gekkoscience-bm1384-project-development-discussion-995675Though if you have $500k to throw around, these things wouldn't be the stumbling blocks per se, as you could talk to a manufacturer or mine operator directly and work out a deal.