Found that going into the system menu, pressing the select button on the individual game and designating a specific emulator and core resolves the problem. Specifically, I chose pocketsnes I believe and this resolved the issue. Been playing several games that originally gave this error by doing this.
@Dinierto I am relatively new to recalbox, but I was looking through the /recalbox/share_init/system/.emulationstation/es_systems.cfg and I saw that there were options to edit the retrieve location for each individual system.
Could the desired result not be achieved in this way, storing roms for certain systems on the sdcard while storing others on flash drive?
@subs
So here is what worked.
config_hdmi_boost = 10
hdmi_group=1
hdmi_mode=16
Uncommented hdmi_safe=1
When setting config_hdmi_boost to anything lower than 10 it bombed fabulously, at least on my 40" screen in my bedroom. And when I say bombed, I mean that it would boot up, and I could choose a rom. But as soon as the rom loaded, the pi would reboot and get stuck in a reboot cycle.
After setting it to 10, everything ran smoothly. I have only tested SNES and GBA roms at this point. We'll see how playstation and others work tonight 
Thanks for all your help!
@subs
Same power supply at each location and with every OS I've tried, and I have tried hdmi safe, which seemed to cause it to work intermittently. I will try hdmi mode 16 and if that fails I will change the config_hdmi_boost. Will update in a few hours with results, assuming my power hasn't gone out by then!
@subs Yes, I see that screen right away typically. It then <sometimes> flashes to the all white screen with the recalbox logo and the word loading at the bottom, but most often it will simply switch to the color gradient screen, then to the recovery mode screen.
Below is the order in which the screens appear, and they cycle through all of these forever essentially. It cycled through for about an hour once.
I've made sure to use the latest build and tried multiple sd cards, and alternate operating systems. The other operating systems I have tried do not have any issue loading, but I would very much like to use recalbox.
Recently installed Recalbox, and I have found that, when trying it on any t.v. in my house, it only fully loads up when connected to an older 32" flat screen television via HDMI.
All subsequent connections to other displays have been HDMI connections as well, no HDMI hubs or source switchers of any kind, not even any extenders in the middle.
The system boots up and flashes through three (sometimes four) screens. An all black screen with the Recalbox log at the bottom, and then immediately flashes to the beloved giant rainbow screen, and then to the page where the config can be accessed by holding the shift key. Occasionally the Recalbox white loading screen will flash on briefly before the rainbow screen comes up.
I've done a fair bit of research and I have tried nearly every combination of display configurations that are available, to no avail.
Also, I can load Lakka up on the same rpi and it works on every tv in my house no problem. I have not tried any other OS as of yet.
Please help, I have princesses in castles who need me!
Hate to necro, but I didn't see an answer to this or another similar question with an answer (though I am admittedly new and have not had much time to dig).
Setting players 3-5 to none in the actual emulator menu seems to have worked just fine for me.