So, how do you turn the system on and off without a keypad? You go, find your phone, login, open the app, then can control the system?
Wall controllers, even those which are years old, are still ideal to have in place when basic controls for a space are needed. They aren't the only option these days for sure, and Bluetooth, as nifty as it is, is also very painful and inappropriate for use in the home. Instead, you want to consider whole house audio sources which are connected via Wi-Fi and allow for network integration. These devices are still controlled from a phone, and can receive audio from your phone, but they are completely stand alone products which work even when your phone is powered off, or out of range of Wi-Fi.
As it is, just because you have 5 volume controls, it doesn't really mean that the old owners had five zones. It may just mean that they had a single source to all the rooms and five volume controls to adjust volume in each room.
So, you need to determine what it is you want to listen to and if you want the ability to listen to different things in different rooms at the same time. Having two or three sources hooked up so you can throw a CD on, if you still do that, or having a his/hers setup of networked audio players isn't a bad thing. If you want to pipe cable TV audio into the system, that's an option as well if you want. But, first you determine the actual sources you want to play everywhere.
On the higher end side of things, go with a multi-zone source selector. A model like the Lync 6 from Home Theater Direct is an example:
Whole-house audio systems you can install yourself and control with smart phones and tablets. All HTD systems include a 30-day guarantee and 5-year warranty.
www.htd.com
You can hook up multiple sources to it, of your choosing, then use your phone to select a source for each room and adjust volume for each room. This makes the volume controls obsolete.
Sources may include up to 6 analog stereo devices like a BlueSound player, or a couple of Sonos players, a CD player, or cable box. Up to six, mix and match, your choice.
Cheaper would be to simply hook up a single source to your amplifier. Like a Sonos or BlueSound product. Replace the Niles keypad with a volume control (if the wiring is there to do so!) and control playback from your phone and adjust volume by walking to each room and turning volume controls up or down as you choose for music playback.
Before buying that very nice amplifier, there were some other options that could have been a bit less money overall, but kind of pointless now because you have the nice multi-channel amplifier. I've used Sonance stuff over the years, and it is really solid equipment. Not inexpensive for sure. Hopefully you didn't buy the 1250 brand new.