Need recommendations for loud but cheap battery-powered wireless speaker

I need to get a wireless, battery-powered speaker.

Requirements
  • As loud as possible for spoken voice. Preferrably greater than 110db SPL
  • No need for sound quality, or strong bass. Just volume.
  • Under $400, the less the better.
  • Battery-powered
  • Bluetooth or other wireless connectivity

If anyone could recommend a speaker for me, I'd really appreciate it. The cheap PA systems rarely give any specs that could be used to judge how loud they get, and only have exagerrated peak power specs.
 
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I know next to nothing about PA, but this guy seems to have tested a bunch of different portable PA systems:

The QSC CP8 that he measures at 109 dB is over $400 new, but you might be able to find it used for less.

His test methodology is to turn up the volume until just before the clipping light comes on, but that's with full frequency music. Since you're only doing voice, you could add a high pass filter (some units have built in EQ) and likely crank the volume higher before you run into distortion or x-max. That might allow for a cheaper option while still achieving your targets.
 
I know next to nothing about PA, but this guy seems to have tested a bunch of different portable PA systems:

The QSC CP8 that he measures at 109 dB is over $400 new, but you might be able to find it used for less.

His test methodology is to turn up the volume until just before the clipping light comes on, but that's with full frequency music. Since you're only doing voice, you could add a high pass filter (some units have built in EQ) and likely crank the volume higher before you run into distortion or x-max. That might allow for a cheaper option while still achieving your targets.
That's not battery powered though.
 
The Bose S1 Pro is available with a rechargable battery and the Alto Busker is battery powered by default. There are more of this type speaker showing up all the time now, they are targeted at busking musicians and usually have all the necessary options for that built in. EV just released the Everse 8"and 12" versions for example, I was playing with the 12 just the other day at my dealer but even the 8 is rated for 121dB which is far more than most of the other offerings that size.. The Alto might be the best low cost battery speaker available that will deliver some level of professional performance, below that you get into disposable junk pretty quickly. As with most tech things you get what you pay for with these things.