Consider a better wired connection instead of temperamental Bluetooth.
Basic automatic AT-LP60X $105 > 3.5mm aux cable > 3.5mm Aux input on the soundbar.
Or a better manual AT-LPW30TK $175 > RCA to 3.5mm cable > 3.5mm Aux input on the soundbar.
Or if you won't have the turntable near the TV and soundbar then either turntable > included audio cable > pair of powered speakers and they have Bluetooth for playing music from your phone, tablet or computer:
You can get an additional passive volume control such as this:
To reduce the volume on your SE215s (connected to the output of this volume controller), for when you turn the volume of your E-drum to the highest to record.
You will also require an additional aux audio cable such as this, to feed the headphone signal to the above mentioned Volume Controller:
Which part of LA to search a 30 mile radius, chat or PM with a zip code.
Compact amps with analog input for the turntable plus Bluetooth:
Full size stereo receiver https://www.accessories4less.com/make-a-store/item/yamrs202bl-rb/yamaha-r-s202-2-ch-x-100-watts-natural-sound-stereo-receiver/1.html with remote, analog input and Bluetooth.
Plus speaker wire, pure copper oxygen free 16 AWG. Then How To Strip Speaker Wire and How to Install Speaker Wire.
Neither. You can do better buying the turntable and speakers separately.
Turntable:
Better powered speakers with Bluetooth for a smallish size room:
The G-Boom has 3.5mm Aux input so you don't need to pay more to have a Bluetooth transmitter in the turntable.
AT-LP60X $88 > 3.5mm to 3.5mm aux audio cable $6 > G-Boom speaker.
Or a better automatic turntable that costs less than the $219 AT-LP60XBT: AT-LP3 $165 adds adjustable tracking force.
Or a better manual turntable for the same $219 cost of AT-LP60XBT: AT-LPW30TK $219.
Or for the cost of the $219 AT-LP60X you could get the AT-LP60X and a pair of powered speakers with Bluetooth:
AT-LP60X with 3.5mm output? 3.5mm aux cable into the sound bar or get an RCA to 3.5mm adapter.
Good plan. The AT-LP60X is easy to use and will last through a speaker upgrade or two. The AT-LP60X has 3.5mm output and includes a 3.5mm to RCA audio cable. If the Bose has 3.5mm input then you will need a 3.5mm to 3.5mm audio cable.
Is it a plenum ceiling? If so, you can't install any speakers into the ceiling that are not plenum rated and designed for that type of environment by electrical code. This includes the speaker wire itself which MUST be plenum rated.
If the ceiling space is not a plenum and can use anything, then the Monoprice speakers are MUCH higher quality than the Pyle stuff which is just garbage. Pure garbage.
If you need plenum speakers, there are inexpensive options out there, but you need to know for sure what it is you're dealing with. Then, I would get a small quality amplifier like this one which can sit under the ceiling near the projector like this one...https://www.ebay.com/itm/265941981015
That will give you proper amplification for any 8-ohm speakers in use. You can use a 3.5mm to 3.5mm stereo audio cable to connect the amp to the projector easily.https://www.amazon.com/Amazon-Basics-Speaker-Subwoofer-Gold-Plated/dp/B00NO73MUQ/ref=sr_1_6
If the space above the ceiling is a plenum, it will violate fire code, which can hamper insurance if it is ever needed, so it is legally required to use proper wiring and speakers in such a situation, and you should know what you are working with. In such a case, you will need a commercial speaker as well which can go up into the plenum. They tend to cost a fair bit more money (about $100 per speaker) to do this. Or you can mount speakers inside the room and just surface run cabling, or get plenum cabling to feed them. The amplifier cannot go into the ceiling if it is a plenum space.
If there are air returns in the ceiling which are not ducted, then the ceiling is part of the air handling space, and is a plenum that requires that added consideration. Something like these would be a fairly inexpensive option and they include plenum rated speaker wire which can be run to the amplifier I linked above...
https://www.amazon.com/Dayton-Audio-CSK658-Plenum-Speaker/dp/B002TVPVU2/ref=sr_1_6
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