You can have injectors pop tested.
But if I were you I'd first try and change the injection pump static timing a bit and see what that does.
The injection pump mounts to the back of the timing gear housing with 3 nuts, they are not easy to get to!
With engine turned off loosen the 3 nuts, no need to take them all the way off. There will be a mark on the top of the injection pump mounting flange and maybe one on the timing gear housing, note where these are before you loosen anything, good idea to scribe a mark yourself. I would try turning the pump towards the drivers side, this retards the timing, only move it maybe 1/16" inch, going by your marks, about the thickness of a dime.
Do not do anything with the bolts that are on the timing gear housing, cover, the 4 bolts that point straight up, do not touch. If you are not clear on this ask and or do a search. So, move the pump a little and tighten the 3 nuts and see how it runs, if it makes less black smoke you are on the right track.
Hopefully somebody can explain this better than me!! It's been 10 years since I did this

If moving a little bit helps your black smoke problem then I would take it somewhere and have the timing set with a timing tool.