How would you Write the Kett out of the series?

Doubt it. Exaltation as we know it may "cure" the genophage but on the other hand all Kett we know of are sterile. No sexual reproduction, only reproduction through exaltation.

I really don't know why you'd write them out of the series this early.  There's a lot we don't know about them yet and they can always be made more interesting by fleshing them out in different ways.  If Bioware wants to write them out of the series, the easiest way would be to have the Initiative lose heart and simply give up on Andromeda, have the remaining survivors go back into cryo on Nexus and return to the Milky Way now 1200 years after they left.

If not writing them out of the series and continuing with a story in Andromeda, I would potentially go with this:

As of the end of ME:A, Primus is poised to take over as the Kett leader, but nobody knows his background.  We do know that he's was stirring the pot of discontent among the kett.  For argument's sake, let's say that the kett actually figured out how to exalt humans and asari shortly after Nexus arrived in Heleus and that all kett ascendant were asari (and their exaltation shield is an adaption of the biotic barrier).  Kett Destined could be exalted humans (based on the infiltrator profile, with sniper rifle and cloaking ability).  Instead of the Krogan being the first species the kett figure out how to exalt, they are the second last and the Salarians are the ones giving them real trouble.

Let's say, Primus was dear old dad, who remembers his old life a little more strongly than the rest and who has been honestly working to undermine the Archon.  We are now perhaps poised to create an additional alliance with the Kett against a greater enemy threat - the Jaardan or to have to go to all out war against our own father.

At this stage, we know absolutely nothing about the Jaardan other than they had the technological ability to create the Angara and, perhaps, the Remnant and they were attempting to revitalize the cluster when they were attacked by an even greater enemy (or the scourge).  We don't know what the scourge is doing to adjacent clusters and potentially to the Milky Way (if what started it is the firing of the Crucible).  Unknown to us, we're in a race to stop the scourge from completely destroying both galaxies.  We need to figure it out and figure out a way to get back to the Milky Way as well.  Creating some sort of fast-travel mechanism between Andromeda and the Milky Way is key.  Ultimately the game covers two galaxies and we have a a multitude of new species we haven't met yet and places we haven't explored yet.  The possibilities are endless.

I don't think I'd write them out, but I might create a species that poses an even bigger threat. I would make two or three new races in neighboring clusters who would help us fight the Kett and the new threat. Andromeda doesn't have relays so travel is a bit limited.

Primus is interesting, isn't she a former Angaran? She looks just like the Cardinal. I can see her not being the main baddie but I can see her reporting to the Senate and maybe the Kett main bad dude is a general or something, or some Uber powerful Kett wizard guy.

That’s true I didn’t think about Meridian. It’s possible but I’m still not a fan of going back.....yet. Too much left to do in Andromeda.

I agree.  One thing that caused me to put together my musing about dear old dad being the Primus is the similarity between the trailer and the end of the game.  In the one trailer, we see an N7 turn away from the galaxy map and walk directly towards the screen.  At the end of the game, we see Primus do almost exactly the same thing.  I can't help but wonder if Bioware wasn't actually foreshadowing that the two are one in the same.  N7 = dear old dad; Primus = N7... Primus = dear old dad.

The second thing is that I question how it was possible for Archon to obtain a hollow of Alec communicating with the monolith on H7.  He wasn't there when Alec did that nor was there any indication of any of those little flying things being around to record the event.  I think Alec did survive and was taken by the kett and asked to repeat the feat... only he couldn't really do it because SAM had already been transferred to young Ryder.  The only visual thing out of place is Alec's helmet, which is on him during the hollow scene... unless that's actually young Ryder's broken helmet... but then I can't explain why the visor appears to be intact in the hollow (Still Bioware might have just been trying to disguise the situation so as to not completely let us in on that story line until a second game.

Part of me also wonders if the story in Andromeda is really just the set up to continue with Drew's dark energy problem in the Milky Way.  Meridian, as we know, has the ability to revitalize at least one entire cluster (at least for a time).  ME2 started to set up the Milky Way as a dying galaxy due to dark energy:

ref:  www.eurogamer.net/articles/2013-06-19-ex-bioware-writer-discusses-dropped-ideas-for-mass-effect-trilogy-ending

The above is a quote from an article where Drew was describing the dark energy plot.  Part of me thinks that the sojourn to Andromeda might have just been Bioware's way of connecting everything together and, perhaps, giving us some means to "fix" or "prevent" a dark energy disaster in the Milky Way.

They have an empire. It wouldn't be possible to just write them out without leaving a huge void in the narrative. An empire doesn't just disappear, unless of course they were completely wiped out by something worse, in which case, how do our allies deal with that without another Reapers v Crucible scenario?

Shouldn't we answer the "why" before jumping into the "how"?

I wouldn't write out the Kett, the only thing I'd write out is the instant Kettification. That was absurd, and should've taken longer to feel more real rather than fantastical.

I liked a lot of the rest of the Kett, and I'm still intrigued by the message between the benefactor and kett.

I'd agree with that, the letter involving Benefactor & Kett mentions that they visited his homeworld. The question is... how? Perhaps there are Jaardan ruins in the MW too, and some kind of gateway linking the two galaxies.

I'm half expecting Ploba to not be a 'Jupiter brain' but to be the MW end of a gateway

That might work, or that it's the last serum in a list of various other procedures.