You can keep unwashed emulsions for a long time if refrigerated with no detectable photographic effect. I have some two years old samples in my fridge and when I used them last time they were just like the day I made them. But this requires (1) proper emulsion formula for unwashed use, (2) proper emulsion stabilizer and (3) biocide. The problem with unwashed emulsions is that ripening continues during storage. Overripening leads to fog and loss of speed and contrast. You must stop this ongoing process by using proper stabilizer. Use of formulae that are suitable for unwashed use is also a big help. Usually, chloride emulsions (including chlorobromide and chloroiodobromide emulsions) are quite usable unwashed, if the formula is adjusted properly. Bromide emulsions are in general much slower and doesn't keep as well, if used unwashed. (There are ways to do this but you'll need a ;lot more elaborate setup than washed process.) I'd use benzotriazole as the stabilizer if you don't have access to anything better. Generally, for bromide emulsions, there are much better choices but they are not very easily available unless you have an account with lab chemical supply houses.

In reality, if you want good, fast emulsion of good contrast, you're better off mastering the washing process. There is no way around it if you want faster emulsions.

I bet commercial liquid emulsions are all washed, and probably all bromide based. They also most likely include proper emulsion stabilizers and biocide. When made properly like this, the emulsion is quite robust unless you contaminate or expose to light.

Biocide is necessary because bacteria and fungi can decompose gelatin and physically and chemically change the gelatin. Bacterial growth slows down at refrigeration temp but does not stop it. Fungi are also more resistant to lower temp. I use o-phenylphenolate or 2-phenylphenol sodium salt with good results. I have more info on the wiki section of my website.

Did you use pepper fog with deionized water? When you mix silver nitrate with tap water containing chlorinating agent, some insoluble silver compounds form (looks cloudy) and they may provide an effective nuclei to grow on, providing a big fog center. I wouldn't use that kind of water. If water is perfectly fine but still get pepper fog, that's probably because of poor quality gelatin. The best is to ditch that gelatin and get a different batch of inert photographic gelatin. Also, too little gelatin (less than 0.5% in the kettle) or ineffective mixing can cause pepper fog, but these are rare based on your formula.