Thanks, everyone, for your help. Problem is solved now! I removed the DirecTV green label splitter (I had tried all possible combinations of the DirecTV splitter, the DirecTV SWM, a non-DirecTV 4-way splitter, and the ibyone AC-powered amplifier) and got a distribution amp I bought at Lowe's in the TV cabling section (thanks for the suggestion on the direct-connect amplifier, harshness! Walmart did not carry these amplifiers in the store, nor did Home Depot) that replaces all splitters. The line from the satellite gets plugged into this amp, and the lines to the TVs also get plugged in directly to the amp. That gave an extra 10 dB per TV line, and raised the channels available to about 40. Worked perfectly!
Only weird quirk (for anybody that comes across this post in the future): we're about 45 miles from both NYC and Philly and neither city's Fox stations come in at all, although they should at that distance. The antennas are in the same places as the other stations (that come in strongly) in both markets. Fox must use under-powered signals in both cities. Bummer, as it's Super Bowl Sunday and the game is on Fox! Will jury-rig a screen cast from a website carrying the game.
One note of caution for anyone buying a 1byone product: their customer service is incredibly poor. I ran this entire initial scenario past them via their email help service. It took them nearly a week to respond, and when they did, they merely asked me for my "order number" to "help" them provide better assistance; no other help provided. I had supplied them with all product numbers and my eBay user name (as I bought it through eBay and they asked for that if it was purchased through eBay) when I submitted my question. That was a strange request as their product is their product, no matter where it was purchased. Expect zero help, and a significant delay to find out they offer zero help.
The SatelliteGuys board comes through AGAIN!