I don't like to cut 'em but I believe it's a personal thing.  I'm deaf as a post, especially my tonal range, so I gave up on music a number of years ago.  Don't like it but that's the way it goes.  So, my Model 2 Retro works great for me and gives me BT phone which I love. 
If the tunes are that important to you, hack it.  Done neatly, and from what I can tell that's your style, it will look fine and make the car what you want. 

BB1

If you have a custom center console, could hide radio in there.
And could be hidden when parked.
Easy to do if you have an aftermarket A/C, heater, defrost combo in place of stock heater box.

Mine is in glove box...cassette player and controls 10 disc changer in trunk.
Yeah it’s old but sounds much better than any of the stock radio replacements.

Or get stock radio converted to modern internals.
I want to see how these conversions last before spending the money.

I have seen some done nicely with modern radios.

Another option...
Some of the new stereos have a faceplate that can be remotely mounted from the receiver housing.
Kinda like an umbilical cord.
Then faceplate attaches via a plate to stock radio holes without cutting.
Either by bolting bracket on or by magnets to stock location.

I didn't care one way or the other on having a stereo in my 69. But my son wanted to install one so I let him. It kicks a$$ but I only listen to it less than half the time. Drove to Waco and back without turning it on. Like Bullet Bob, I love the blue tooth feature.

If you decide to cut your dash and the next owner is horrified, they can fix it along with the other mods they don't like.

You plan on entering it  in a concourse e'elagonte show any time in the next 20 years?!  (Didn't thank sew!!)
                              'Go'ta goug'in' ....your car...your choice! 
My phone with blue tooth ear buds blasts out the Drifters/The Tams/Ben E King/other Carolina Beach Music tunes that still-thrill-my drill (If you get my drift! )
6s6

So show us what you stuffed in the trunk.
 

Since mine was cut when I bought the car in 1992, it is now fitted with a single DIN bracket, solidly mounted. It requires no rear radio support bracket since it is solidly attached to the dash face.  I gave gotten used to the look of the newer radio, and I enjoy the convenience of phone and USB ports.

I rarely turn it on to listen to music.
That comes from under the hood.

Here is my finished project, at least until I modify again. 

Well what can I say, it COVID. I am so bored my brother wants to bring his 66 vette over and have me swap out the stock AC for Vintage Air. He said I need to step away from the Stang. LOL we will see
Also I discovered the short after installing the relay I found its the iner horn contact. They seem to move around quite a bit. Going to order a new one

BB1
I have an Otter box case for my phone that has silicone rubber outer.
It fits nicely between radio buttons and ashtray.

Open up ashtray, set phone on it, slide ashtray close to clamp in place.

Ended up doing that while using GPS speedometer app for calibration after I had changed rear gears.
I just don’t use my phone for music like a lot of people do.
I use it more as internet computer and  a camera for projects...how does this go back together? 🤣🤣🤣
Maybe someday....yeah right.

Chris
What kind of mount is that for radio?  Just wondering. Marine application?