Honestly, even after looking at it, I still find it relatively easy to imagine a game where calibers are used instead of weapon damage values.
Of course it works. Just a different solution to apply damage codes to weapons. But if you are looking for some acceptance for your homebrew you should consider to make not that many changes to the existent system. Tweaking stats is not only more work, but also makes it less compatible with future releases because of constant conversion required. Not to mention those people (essentially those with who you play) who do not like how you tweak and convert. Something practical should be build on top of the current rules.
The biggest issues with this are the sniper and sporting rifles, which have damage values that jump all over the place.
You might assume these guns using less common calibers and associate them with special purpose cartridges. Pretty simple and not unusual for both firearm classes.
I went all the way you are currently going. Investigating SR firearms, reading about different more or less common calibers, working out different approaches and cramming my desk with tons of notes. I had fun doing it because I love keeping my brain busy in my free time with such stuff. And although I never seriously planned to pick up this house rule at my table I asked my players to assess. Expectedly, feedback was not that good with counterarguments meanwhile being well known and absolutely valid.
Namikaze made a good point here. Abstract the system as much as possible and do not be afraid of compromises reflecting less realism in favor of playability. My suggestion on page 2 of this thread is the current state of development I came up with after getting to this realization.
Keep it simple, stupid 
I hope this helps - at least a bit - to find your very own key to the implementation of calibers in YourGame™.