1950's Vocals

What has improved in music and sound that I would need to.... reverse, so to speak, to get that 1950's/1940's sound in my vocals?

The idea that there have been no technological improvements is pure nostalgic nonsense. Nostalgia often normalizes technical limitations as ideals rather than the barriers they were. In film, 24 frames per second was not some magical ideal but a practical standard we are now used to. Most people the. And now would certainly choose stereo over mono.

With that said, the ideal way to approximate that sound would be via literal usage of vintage equipment. Otherwise you are looking at the poor facsimile of plugins emulations

While using old 50's gear would give you the best results, it would require remortgaging your home to buy it or finding someone else who has it and probably charges a fortune to use it. So it isn't practical. Let's work with what you have accessible to you as I suspect that's probably what you want.
 
I have found what works best for any vintage sound is not to use old or crummy stuff you have lying about unless it really is vintage. Instead, use the best gear you have and record a good, high quality, modern sound to start off with. That might sound counterintuitive, but what that will let you do is accentuate the qualities you are looking for and reduce the ones you aren't. Obvious plugins to use would include a tape emulator, consol emulator and valve saturation as well as EQ of course. Recording in the 50's used a much more simple set of gear. Usually just one or maybe two mics with the mic position in the room being used to create the mix. There were no big consoles with loads of channels and usually only 1 or 2 tracks on the tape. They had pretty basic effects and signal processing too. So avoid modern compressors and make the most of the tape, console and valve saturation for compression and subtle distortion. Don't be afraid to run it through multiple tape sims either with subtle wow and flutter and other tape characteristics such as hiss. A bit of degraded analogue slap-back delay should finish it off. Use a good reproduction of an original 50's recording for reference and you should be able to get pretty close.

This is about the closest thing to a 1950s studio that uses 1950s techniques there is. Well worth watching the video.

https://www.soundonsound....es/recording-50s-style

With the exception of the room, microphones and “mixing by microphone positioning” most of it can be emulated in a DAW. Pultec style equalisers, LA-2A compressors, tape emulation and working in mono can get you a long way towards a 50s sound.

Waves Abbey Road plugins, especially the REDD desk, J37 tape emulation and plate reverb are intended to emulate the technology EMI were using back then and sound pretty good.

Start at the front end - ribbon mic.  Soft top end.  Run through a pre or front end hardware w/ transformers.  That too can roll off the top, soften the transients and thicken up the whole tone.
 
I have a $50 mxl ribbon that works magnificently on guitar amp.  And it is OK on vocal.  Run that through a WARM Audio WA12 pre (I haven't used the new Neveish one) in a small dampened room.  I bet you can get close.
 

What Jack said. If you use any reverb it would be a structural space or a Plate or spring. 
But the sound was a clean pure sound and good talent.