Been chasing the perfect setup for distorted vocals for quite sometime. Tried so many different setups, some work better than others. Pro studio engineers rarely discuss at length their setups to achieve distorted vocals. Most articles regarding this are at best rather vague. So, here's some of the things I've done.
As mentioned previously, one of the best and relatively simple approaches is a mic (cheap or not) direct into an analog recorder. Serious input gain...good results. Usually, I get it to near total nastiness, and cut input gain on the recorder, just a hair.
Also mentioned early is doubling vocal takes, two or more separate vocal takes. You can take a cleaner approach to get more definition, and get more frequency response in this setup. Cause the more distortion ratio, the less frequency EQ range you are working with as a result. Therefore, knowing where the range of heavily distorted vocals fall in the spectrum of frequency is rather important when mixing with guitar. Trying to create headroom for distorted vocals with guitar can be troublesome...
You can also try to blend one heavily distorted vocal with another vocal take of cleaner less distortion.
Here are other ideas:
Reamping clean vocals to a guitar amp. Or singing directly into amp, with distortion. Older the amp, usually the better. Tube amp usually work the best, but I've had success with late 60s, 70s solid state budget amps. Amps I can recommend: Bassman, Twin Reverb, 70s MusicMan, 60s Silvertone. Bullet mic or harp mics work great...hand placement around bullet mic adds to this effect. Might have to use a de-esser. Mic placement is key in both vocal mic or micing the amp. EQ on amp is your friend!
Using guitar pedals can work, but noise issues can really deter this method. Avoid anything too new!!! Well not, necessarily...Or anything with a wall wart power adapter...ground hum kinda kills it. But, I've used old fuzz pedals, Rat Pedals, SansAmp Bass Driver. Mixed results. ****If you find any setup to your satisfaction---write down and take pictures of your settings. Because, not being able to achieve the setup again really can kill a day in the studio.
A Really cool thing that you might be able to find at a yard sale, flea market etc. are budget mixers from 70s/80s with built in fuzz/ reverb/tremolo/echo. Pretty sure some of the Mummies stuff were done with this method. Even radio shack brand mixers from this era sound pretty good for distorted vocals.
Again, as mentioned earlier, Tape delay/echo/ reverb stand alone units can really add to the thickness of a narrow vocal recording. You can do it direct or reamp a vocal take. Both work, but sometimes its better to achieve this after the fact, unless you have a setup that is working great while recording
Hope this helps! Have Fun!