If your criteria is NEVER tipping over, then yes, ski may not be for you. Being comfortable remounting your boat should be your first task, regardless of what boat or boat type you paddle. If you paddle long enough, everyone tips over. Everyone. The Nelo 600 is indeed extremely stable, but 'stability is in the butt of the beholder' and is a learned skill. Most tandem sea kayaks have a very flay hull with a ton of primary stability. That is what your butt is used to.
A ski inherently has less primary stability, because flat hulls are not ideal for larger or steeper waves. Skis have some flatness to the hull, but probably much less than the typical sea kayak, so as others have said the 2 boats are apples and oranges.
I think you're giving up too soon though. How many things were you good at the very first time? Driving? Biking? Swimming? Writing? soccer? baseball? ice skating? not so much. Those are all fine motor skills that were honed over the course of hundreds or thousands of hours. To expect to be good at something completely new the first time is unrealistic.
I know you say it was incredibly tippy but I guarantee you that was just your perception. Your butt gets used to the wobble quickly. the double aspect does increase the tippy feeling by probably 10x compared to solo, so maybe you just paddle it solo in turns and get used to leaning the boat and letting it roll underneath you. This is natural, but if you're not used to it it can be very unnerving. Once you're comfortable solo, try again together.
The other thing i'd recommend is to let yourself use the secondary stability. Let the boat roll side to side. a 24" boat like the 600 has plenty of reserve stability and is probably much harder to flip over than your initial impression may indicate.
Last, I come from an open canoe racing background (canadian canoe / Jensen canoes / 3x27 pro boat - not those fake olympic canoes
. "Boat Bonding" with your partner over the course of many hours is key to a successful tandem team. Eventually you stop wobble-fighting each other. You get in sync, you know when to sprint or relax and what the other person is thinking, you know when they're struggling, you know what is a normal 'close to the edge' lean and when to 'brace for your life'. That preception comes more quickly if you have other experience, but even 2 experienced racers have their own nuances that the other must learn.
Double ski is the same.
So we'll be sad to loose you if you decide to sell it, but I recommend you give it more than 1 try, and maybe start out solo until you're comfortable with the feel of the roll. You cannot find a more stable ski than the 600