I only provided the Crutchfield link to show you what might be available as far as Bluetooth amplifiers go. I didn't mean to suggest that you purchase through Crutchfield.
The Galaxy S7 has Apt-X Bluetooth, so I would try to get a Bluetooth receiver, amplifier, or head unit that has this capability. The SQ is much better than standard BT.
And I wouldn't discount having or using the USB input. Having all of your music files on an inexpensive removable thumbdrive is great. And most double-DIN head units have a decent interface for this. In addition, USB will always sound better than the same files played over Bluetooth, unless you are using crappy compressed files to start with.
Regarding your setup, although more expensive overall as you discovered, a good aftermarket head unit with all of the features that you want built-in, plus the necessary SWC interface, Dash Kit, etc, would be the simplest and best solution as far as ease of operation & all-around features, without being confusing for other drivers to operate. It will also most likely be much better as far as SQ is concerned when compared to the OEM head unit.
Some of the Bluetooth amplifiers that I suggested have the separate Controller/Display unit that you can mount up front, so that somewhat remedies the problem of losing your steering wheel controls. But that might be somewhat of a fugly set up for some people, or there may not be a good place to mount it. These are more of an option for people who cannot replace their OEM head unit due to it having other integrated vehicle controls, such as the AirCon & Heating, etc.
Regarding that FLI Underground 12" Active Subwoofer
, reviews look mediocre at best from what I've seen. I would wait & save up your money for a decent trusted name brand such as the Alpine Type R 12" or a JBL GTO + maybe an inexpensive Rockford-Fosgate amp. I would always try to steer clear of the lesser known brands that don't have a long-term proven track record & reputation.
That 4-channel Kenwood amp looks decent, but I'd probably want something more in the 75-watt x 4 range. For some reason I've never been impressed with any of Kenwood's amps. But I haven't tried the newer X801-5 & XR901-5, but I'm told that they're much better than Kenwood's other amps...Quite Expensive though!
But a decent 5-Channel amp would be perfect for your setup. It would simplify wiring as well. We have a 5-channel amp available here called the NVX JAD900.5 that is excellent for the money...about $220 USD. I know that several other manufacturers have this same amp with their name on it that are probably available in the UK...PPI, Soundstream, Hertz, Polk, & Nakamichi.
As far as decent car audio gear, I think that it's much better to save up and "Buy Once & Cry Once", especially if you plan to keep the vehicle for any length of time. Start with as good of gear as you can afford, otherwise you'll find that the cheaper stuff probably will not satisfy you and you'll need to spend more money again.
I would really suggest to check the Classifieds & For Sale section of the UK car audio forums such as Talk Audio UK. Gents are ALWAYS upgrading or changing their gear and you're bound to score some good deals on better equipment than you could afford otherwise. This goes for power wire, RCA cables, distro blocks, battery terminals, etc.
Just make sure that the seller has been on the forums for several years and has a good reputation.
Regarding your proposed wiring, what you've outlined is pretty good, but whenever you Change Wire Size, the smaller wires need to be fused separately because they cannot handle the current that the larger wire can carry. The fuses in the amplifier are designed to protect the amp, and you need the fuses on the actual wires to protect the wire itself, and your car.
Make sure that whatever power wiring you buy is real OFC (entirely copper) and not CCA (copper clad Aluminum). Sometimes you really have to dig through the fine print to make sure.
If you can, I would run 4 gauge power wire the entire way, even splitting off from the distribution block (if your amplifiers will accept it).
If going with an aftermarket head unit, try to get one that has Front, Rear, & Subwoofer 4V RCA preouts. These will generally be better made and provide a cleaner, noise-free signal to any amplifiers that you add.
You could simply run your existing car speakers from the HU, and just by a true 350-500 Watt subwoofer amp, until you decide to upgrade later.
Are you just using the OEM factory speakers that are in the car now?
Hope that helps.