Reviewing old versions of the game (Vanilla, season One, season Two, etc), especially the campaign and going through the fandom wikia, I discovered one or another change that occurred in units and that could then be considered viable to rescue the janissary.
In the abbasids, the camel at the time of departure had a very low attack, to the point that it was the same as the current janissary. His bonus was also anti-cavalry. To summarize, here the data

Ok, so we have that the camel rider was very weak…against everything except cavalry. What did the developers do to improve them? Base attack increased and bonus decreased. That should work partly with the Janissaries. So I did an analysis in excel. Let’s first look at the status of the base Jenisaro vs a man-at-arms:
As noted, while only 6 handcannoners can take down an elite man-at-arms, not even 10 Janissaries at the same time can kill one, you need at least 13. On the other hand. If a single handcannonner were to fight an elite man-at-arms, if you manage to hit him 6 shots he’ll take him down. The janissary on the other hand, not even in 20 seconds does it. Consider aside, that the handcannoner has 130 HP, while a janissary has only 90 and 105 elite!
Anyway, to solve it I created 2 versions, considering the rounded attack bonus they would have when developing chemistry (+20% attack, which usually rounds up).
With version 1.1 at least they are able to get them down in the elite version if they focus on 10, and in post-imperial they only require 9 hits to get down to one, and attack the next one, whose attack speed stands out.
With version 1.2, the change is only slightly more minor, they require 1 less attack, but the anti-cavalry bonus has gone through the roof.
On the other hand, with light armor units, in the case of spearmen, the result is more than optimal:
It only takes 4 handcannoners to beat one hit spearmen, 8 janissaries in the current version, and 6 with my version 1.1 and 1.2. I believe that the advantages are significant with the modification that I propose.
Oh, and of course, PLEASE increase the Janissary’s HP from 90/105 to 100/120, or 95/115. I think that’s actually the biggest weakness they have. They are the only gunpowder unit that has such a low HP, even considering that they have an elite version.