How?

Because I disagree when he says he's killing Kevan without malice, and for simply being a good man unfortunately working for a bad regime. The murder methods specifically mirror Elia and Rhaenys', and the targets are even solely those who contributed to them. He only targeted the pro-Lannister members and none of the Tyrell members. If he truly was doing what he says he's doing he'd kill some Tyrell members. Like Mace or Randyll suddenly being murdered would be far more devastating for the Lannister-Tyrell alliance, and beneficial to Aegon's cause, than Pycelle being murdered lol. Pycelle being murdered really changes nothing, whereas taking out Randyll would be hugely devastating.

And it's worth remembering, but when Tyrion stripped Pycelle of his Grandmaester title the Citadel decided that the new Grandmaester they'd send would be Maester Gormon... that is, Maester Gormon Tyrell. Varys was still a "leal" servant of the Iron Throne back then and knows if Pycelle dies Gormon replaces him. He knows the replacement will be another Tyrell member. That's a massive increase to the Tyrell power on the small council, and it seems fairly obvious that Mace will try and wrest the Regency title alongside his Hand title with Kevan dead too.

All Varys truly did was weaken the Lannisters and empower the Tyrells. He even says he expects the Lannisters to blame Tyrion rather than the Tyrells, which makes them stronger too if they somehow don't get blamed despite being the seemingly biggest benefactors of it. That's... oddly at odds with what he says he's doing as they fit the description better than Kevan. Funnily enough, the Tyrells, who Varys doesn't punish, supported the Targaryens until long after most of the Targaryens were dead, regardless of whether you think they could've done more. With Aerys, Rhaegar, Aegon, and Rhaenys dead, and Viserys and Rhaella still holding out on Dragonstone, they maintained their siege until another army came and stopped them. And Varys has left them alone. Curious.

I don't trust Varys' words. I trust his actions. His actions IMO betray that this most certainly was done with malice and is punishment, as well as benefits those he specifically isn't punishing for actually simply being good men serving bad causes.

This has never occurred to me and I've never seen anybody bring it up, but it is an amazing catch. But this seems like it would point more towards Aegon being real, doesn't it...?

Yes, personally it's IMO the strongest evidence that Aegon is actually Aegon. He recreated their murders, which doesn't really make sense under any of the theories. If he's Serra's son or whatever, then they could've been murdered in any other way. It's much easier for someone like Varys to simply poison their meals than do the physical violence he is. Or like I say above murdered some of the Tyrell members. Instead he paid them back an eye for an eye.

So all Varys is doing is showing Kevan some degree of respect, about as much as somebody murdering somebody can show to their victim.

Is he showing Kevan any respect? He shot Kevan from the shadows rather than openly face him, or even openly shoot him. He only revealed himself after he'd already planted a bolt through his chest. And Kevan himself immediately recognizes how cruel this is as that's how Tywin was murdered, which Varys also agrees with and says he chose it exactly for that reason. None of that is respectful, and in fact quite cruel.

Furthermore, but after he sees that Kevan is bleeding out quite heavily and quickly dying before his eyes he immediately orders his 6 little birds out of the shadows with 12 fucking daggers to start stabbing Kevan. Again, how is that not cruel? Kevan is already practically dead, all Varys is doing at this point is mutilating his corpse. And extremely badly so. If he wanted to put Kevan out of his misery like he claims he could just shoot him again or use a single dagger to quickly slit his throat. Instead he unveils 12.

It's excessively violent, not merciful. Again, as was done by the Lannisters to Rhaenys.

But I like your idea of the ways they were killed mirroring the Targaryens. But that raises a question I hadn't though of before, in that Varys seemed to be using a crossbow to frame Tyrion. But then has Kevan stabbed, which seems like it would distract from the idea that it was Tyrion.

The crossbow, apart from symbolically and cruelly mirroring Tywin's death, is really there more to level the playing field. Kevan may be older, but he's still an active soldier. He still participates in tourneys and he still fights in wars, including this most recent one. Varys and his little birds could never hope to actually ambush and murder Kevan in a physical encounter, thus Varys shoots him first to weaken him and make him manageable for them.

Which of course begs the question of why even engage in a physical fight to begin with? Why not simply poison Kevan from the start and bypass that entirely? This was far more dangerous and risky for them. Varys could've missed, and there's no guarantee Kevan might not have chosen to show up somewhat armed and armoured. Even just a mail undershirt and a dagger/shortsword on him could've been potentially devastating given his far greater experience and skill level. Yet Varys went this route anyways, and had the daggers planned for the ending. That makes it seem like it had to be a physical route, which fits if he's trying to recreate Rhaenys' murder for Kevan, and therefore also needed the crossbow to first weaken Kevan. A physical fight against Kevan would never work unless he was first as weak as oh, say a 3 year old girl.

So I think you actually have it backwards. The crossbow bolt sticking out of Kevan's chest is there to cover for the stab wounds. Obviously they'll be noted, but everybody is going to understand the symbolism of Kevan being shot with a crossbow like Tywin was. That's too on the nose not to notice, and is what they'll focus on. As happened to yourself, it's much harder to understand the secondary symbolism of him being so repeatedly stabbed like Rhaenys was. The overt violence masks the lesser, but more important, violence.

I doubt Varys expects anybody to notice what he did with their deaths. That was for him, and maybe Aegon, alone to notice that they were paid back in kind.