Hey Jim,
Here's a setup pic I took after a race I timed a few weeks ago...

Those mats are maybe 10-12 feet apart or so. I usually just pick a spot beyond the first row simply based upon my intuition. That has always worked for me!
Late reads haven't been an issue. Fortunately the first row gets 98-100% of finishers in most races. The >2% that the first row might miss usually aren't wearing their bib correctly or simply wouldn't care about a late read anyway.
Remember, many of us are timing fun runs and charity events where no one's gonna know or care about their time maybe being a 1/2 second slower.
If the race was that serious, the race director wouldn't/shouldn't be relying on chip timing for accuracy in the first place.
They'd use a line scan camera (like the purple Finish Lynx camera on the tripod in my pic) which is way more accurate than any chip system by far (0.001).
The Finish Lynx camera is overkill for these fun runs where no one's gonna complain about their time anyway. But I always like to set it up as a backup, just in case. Plus it's my favorite toy :)
In high school cross country, I always decide the official results based upon the Finish Lynx photo finish anyway, not the chip reads. And it's always there as a backup for my serious road races in case there's any question about chip reads.
I haven't gotten any cross talk or interference. I space out the mats and side antennas far enough apart to where they don't interfere with each other. Plus, the Impinj readers are designed to automatically sense when there are other readers nearby (e.g., two R420s). And when the readers sense each other, they automatically use completely different frequencies to help prevent interference.
Not only that, I alternate polarities when I setup multiple side antennas. Some of the side antennas are LHCP (left hand circular polarity) and some are RHCP (right hand circular polarity). That further prevents any interference. For antenna cabling I use LMR400-UF which is pretty low loss, thick/sturdy and good against interference. For ethernet, I use shielded CAT-6A which is also pretty good against electromagnetic interference. I spare no expense on sturdy cabling because it gives me peace of mind.
For chips I use two vertical chips on the front of the bib (about 5 to 6 inches apart).