The firearms in the DMG are reasonably straightforward and balanced. With a couple of additional elements, I think you can make a fully viable character out of them. Here are some additional rules to help with that.
One caveat--my goal is to make this mechanics-balanced, not historically realistic. As it stands one shot every six seconds with a Renaissance-era firearm is already unrealistic, but so are four shots per six seconds with a heavy crossbow. I'd prefer to suspend disbelief in favor of making the weapons viable for a character. If you want more realism, assume these are breech-loaded firearms whose design was accelerated by magic or something.
Optional Firearms Rules
Misfire: This quality applies to all firearms. On a natural attack roll of one, your firearm jams. The attack automatically misses, and the weapon cannot be used again until you spend an action to unjam it. This requires a Tinker’s Tools check (DC 10). If the check fails, the weapon is broken and must be repaired out of combat during a short or long rest.
Gunnery: When you take this fighting style, you gain a +1 bonus to attack rolls when using ranged weapons. If you are proficient with Tinker's Tools, you can take a bonus action to automatically clear a misfired weapon without requiring a skill check.
Firearms Expert: When you take this feat, you gain the following benefits:
You gain proficiency with two firearms of your choice, as well as with Tinker's Tools.
You ignore the loading quality of firearms with which you are proficient.
When wielding a one-handed firearm, being within 5 feet of a hostile creature doesn’t impose disadvantage on your ranged attack rolls.
The above makes DMG firearms viable for a character with extra attacks, while not making it OP compared to crossbows or longbows (lower range, louder, expensive). It also adds a slight downside in misfire--even with the fighting style, you still automatically miss on a natural 1 and need to burn a bonus action. But it's not enough to cripple the character.
Any thoughts?