The needed power depends on how loud you want the audio. Of course, crossovers do have some loss and so that will also add to the required power for a given sound level. And depending on your BT source device, you might be able to select a mono output. That would make it easy.
Another option would be to see if you can get one of theos BT speaker boxes that have the amplifier and speakers already destroyed by constant loud blasting. Then you could get the BT receiver free, just for digging it out. That could be the cheapest option.

 

So, to close this out. I purchased a bluetooth only board which also required 5V (4.2). I inserted the board in an independent circuit and it worked great in any setup irrespective of amplifier or speaker output - mono. I skipped the mono circuit by using a 3.5 mm out to 3.5 mm in on the amp board and used a 3.5 mm stereo to mono adapter inline with all that. Great.

Then, I breadboarded the voltage step down circuit using the linear regulator depicted above. I could never get it to work. Even fried one of the BT boards (purchased two) in doing so thinking the circuit was dead and increased the voltage out of the power supply. smoke and wonderful smells.

Taking advice, I am going to finish the build and simpy operate the input device in mono (in most cases, a smart phone). I was trying to avoid the switching from mono for this singular device and back to stereo for all others but doesn't look good from here. Thanks for all input.

 

...and...i discovered after making the decision that I can create shortcuts in iOS to make the mono toggling easier than clicking through menus.

 

The Dayton Audio amplifier uses a Tripath amplifier IC. But Tripath went bankrupt (they lied about the spec's). The IC might be copied by a Chinese place now.

Amazon sells clothing and shoes. Their sellers know nothing about the Chinese Bluetooth thing.
Who says 5W? The description does not mention an amplifier IC part number which might be a PAM8403. With a 5V supply, each channel produces 5W into 4 ohms when it is clipping like mad producing horrible distortion. It produces only 2.5W per channel into 4 ohms or 1.2W per channel into 8 ohms at normal low distortion. If you parallel its two channels then it might destroy itself but it will not produce more power into one speaker than one channel.

You smoked the Bluetooth only board by shorting together instead of using resistors as a stereo to mono mixer. You should NEVER short outputs of anything together.

 

The sad fact is that some boards are not tolerant of over voltage. And the reality is that Using an LM7805 regulator is a bit tricky, because without the proper bypass capacitors they will oscillate and deliver a higher voltage. It is a case where the application notes are to be taken seriously. Using an LM7805 voltage regulator requires two 0.1 MFD capacitors installed close to the input and output terminals. And correctly applying a regulator means that the load negative terminal wire connect to the regulator terminal, and the load positive wire connect to the output terminal. The supply wire must connect to the positive input terminal, the supply negative must connect to the regulator negative terminal. AND, before connecting a sensitive load, verify that the correct voltage is present. AND also use the AC range of the meter to verify that no oscillation is present.

 

The voltage increase was my doing, increasing the voltage output of the power supply. I believe I had the regulator connected properly but did. I measurement to verify output so there is that and had zero understanding of oscillation. Thank you, MisterBill2.

 

The voltage increase was my doing, increasing the voltage output of the power supply. I believe I had the regulator connected properly but did. I measurement to verify output so there is that and had zero understanding of oscillation. Thank you, MisterBill2.

Oscillation in high performance IC regulators is a result of the fact that they are high-performance devices. They are fast so that they can respond very quickly and hold the voltage constant even with rapid load changes, and also quite sensitive for the same purpose. The result is that any feedback can lead to instability, and impedance in the supply line can lead to that feedback. Thus the need for bypass capacitors. This requirement is not obvious when looking at the basic specifications.
My suggestion for powering your setup is to find a 12 volt non-adjustable power supply and use that for the amplifier. The ultimate would be a dual voltage supply that has both 5 volt and 12 volt outputs. Those are much less common in used appliance stores. And unfortunately, many times it is the 5 volt portion that has the higher current rating.

 

the almost end product - still have a grill to design and build.

Thanks all. End up having little circuit work done on this due to my lack of understanding.

 

It does look good. I am glad it is working.