OK, thanks for the information. That Westell modem-router is indeed wireless-capable.
Your original question was:
How do I connect my new R6200 to my Verizon FIOS without having to use the R6200 connected to the Verizon 9100EM router (router-to-router)?
Do you mean by that, that you want to *not* connect the Netgear box to the Westell FIOS box, with an Ethernet cable, but rather want the two to work together wirelessly ?? because if so, that just cannot be done. Except using the Netgear router as a crippled sort of 'wireless range extender', a mere repeater for the wireless capabilities of the Westell FIOS box. And you would not find that useful, not for faster Gigabit access... ultimately the Netgear's capability would be bottlenecked by the Westell's lack of high-speed wireless capability.
If you mean something else, please be clear - what is the router-to-router configuration that you wish to avoid?
..... Also, you raised a question or issue: what causes the network to drop when watching movies over hardwired PS/3, what causes wireless to drop out on phone and tablet... the wireless dropouts could be settled fairly simply, by trying them on just the Westell's wireless alone. That way, if that drops out too, then the Westell could be defective/'broken', and if that does not drop out too, then either the Netgear is defective or, perhaps, it might be wrongly configured for best results. (Since I'm not sure how it *is* configured at present, I have to hedge that judgement a bit.)
So tell me about the router-to-router that you want to avoid, and try turning Off the Netgear and just using your phone and tablet on the Westell FIOS wireless, and see how that goes, and let me know... at your convenience of course. Take care of yourself by preference, but get back to me on this when you really can.