This is often attempted, but usually abandoned for the reasons you have run into.
First of all don't put speakers in that cabinet. Those consumer, radiograms as they were called were just awful. The turntables used crystal pickups. A modern turntable will feed back to the speakers and howl.
Next issue is that modern tables come on a plinth, and that would have to be mounted in the cabinet. It never looks very good.
Now in years gone by in the UK, firms like Largs of Holborn and Imofs also a number of others, made cabinets to take the finest equipment available. They did not take separates, but pre amps, radio tuners and power amps in the bottom of the cabinet. The electronics was nearly always for either Quad or Leak. Their equipment could be mounted as you say. Peter Walker owner and designer of the famous Quad gear always designed his gear that way even after others had long abandoned it.
Turntables back in the fifties and a good deal of the 60s came without plinth and pickup arm. The customer or bespoke dealer mounted the turntable, PU arm and electronics. Often a reel to reel tape deck was included, usually from Ferrograph, Brenell or Vortexion. Later they were quite often Revox A 77 decks which in he early years could be bought without case.
So the only way to really do this so you have something to show for it, is to use vintage gear and gear form the UK at that.
You would need a Quad FM tuner, Quad pre amp, Quad power amp. The best turntable, as a lot were made and sold just as turntables would be a Garrard 301, or 401. Then you would need an SME pickup arm of the period to go with it.
Now this is all going to cost a great deal of money. This gear, though old, fetches a lot of money as the collectors are like flies to a honey pot chasing it.
However with really good speakers you would have a system that would be actually better then the vast majority of current gear. What I have mentioned comes from what is known as the "Golden Age" of British audio.
I have pictures of how the Quad gear mounts. You have options of their gear over many years production. It is so reliable that most of the production is still reckoned to be in good working order.
Here is my vintage turntable case. All these turntables were bought by be 50 or so years ago or more. They were all bought without plinth. There is a Quad preamp for each turntable.
The left is a Garrard 301 Decca ffss set up. The center is Thorens TD 150 SME/Shure set up, and the right a Garrard 301 SME/Shure set up.
My design was meant to suggest the era of firms like Largs. Anyone familiar with that era of British audio would make the connection immediately.
Unfortunately you have very limited choices to do what you want with elegance and get a good result. No receivers that are available mount like you want. There were a few American tube receivers that did. They rarely come up for sale and when they do they fetch a small fortune and sometimes a big one.
If you are serious about this, then for electronics your starting point needs to be Quad electronics. That is the most plentiful and not difficult to find on eBay. It is also very good equipment indeed. You will need a Quad premap, Quad radio tuner, and Quad power amp to duplicate a receiver. Peter Walker was always dead set against receivers. And you know what, he was right!
