Avoiding stock wiring and HU

I'm new to car audio and just bought a 2010 535 BMW E60. It has stock cutouts for shallow 8" woofers under the seat, 4" mids in the front door and tweets in the a-pillar.

I grabbed a bunch of three-way dyn sets out of some Volvo C70s (8" 4" and tweets...also have a SA12 going in the trunk) and want to bypass the stock wiring, amp and HU completely and just run the dyns in the stock locations but wire them independently to my Amps and DSP in the rear and just stream BT audio to a dongle. Is this the correct approach/doable? If not, what should I do differently?

FYI I have a bunch of extra dyn speakers if anyone is interested 10", 8", 4", tweets all in good shape

Not sure if there is a "correct" approach, but it sounds like it will work. You don't have to bypass the factory speaker wires if they are already routed somewhere convenient for you. For example it's easy to re-use the speaker wires in the doors because running new ones through the rubber grommets/boots can be a chore.

I assume you'll have your phone mounted somewhere you can see it, so you can change tracks and volume? You might be interested in a Bluetooth remote control that does simple things like volume, next track, pause/play. Rockford makes one that attaches to a steering wheel, but there are probably others out there too.

https://rockfordfosgate.com/products/details/pmx-btur/

If you want to try something different, that car might be old enough that integrating a stereo might not be too hard. There are companies like PAC that offer factory integration kits that would allow you to retain your navigation, steering wheel controls, etc. Finding a kit for that particular car is the challenge, but might make things a little easier for you even if you decide to bypass factory components.

It might be easier to run the factory wires?
if there is an issue you can change to new wiring, and is works fine... then are done and dusted.

(Aka why fix it if it ain’t broke?)

It's very much doable, did exactly the same thing in a E60 just now. Replaced all the speakers with Ground Zero plug+play BMW upgrade speakers, but ran new wiring to all speakers from the trunk. Where a Helix DSP with Bluetooth streaming module is installed, along with amps for front speakers and subwoofers.

This was a car with just the base audio system = no tweeters, just "fullrange" mids in doors and 6,5" in the floor, powered by the OEM head unit in front. = a great incentive to start from scratch instead of messing with the oem setup for integration etc.

If your car has the hifi audio package (code 676), it has a separate amp behind the left side panel in the trunk. Then it would have speaker cables going from the trunk to all the speakers around the car.