There are some basic problems with the idea that a “clear line of succession” can be established here. The Inca monarchy was a complicated affair; whoever was nominated by the King, and got the approval of the majority of the nobles, got to be Inca, not necessarily the son of the Qoya (Queen.)
Now, the fundamental problem with establishing a clear line of succession beyond the direct heir in this scenario, is running the risk of perpetual civil war by some prince who knows he’s only two, or three, individuals away from supreme power.
With regards to the point of expansion, others have already mentioned what I think. The empire had stretched to the limits of what was possible to hold. The wars in the north took a generation to complete, as did those to the east against the Chachapoyas, while the conflict in the south against the Mapuches was left inconclusive. Contrary to what some might think, the Inca did not expand on the basis of brute force, crushing everything in their path. In fact, most of their annexations rested on the willing submission of the weaker states. But the most essential part, and that which led to the capitulations, was the “political contract” which was assumed by both parties the moment the conquered peoples became part of the Inca state. “Reciprocity” is the best term to define it here. The Inca state assumed certain obligations towards the ruling class of these nations; in turn they turned over their produce and manpower to the Inca. The workers worked the lands of their people, and those of the state, in turn the Inca guaranteed them protection, and sustenance in case of droughts, natural disasters, etc. Also, the local lords, expected presents, gifts, etc. whenever their military aid was needed. (When Wayna Qhapak refused to give Michi, one of his generals, the customary gifts upon his arrival in Quito, the general threatened to leave the field with his entire force, and head back to Cusco, and even worse, take the beloved war-waka, Wanakauri, with him. Wayna Qhapak, relented and gave in, showering his captains with gold, and else.)
Now, most of this modus vivendi had been in place in the Andes for hundreds, if not thousands, of years. The Incas only magnified the scale of reciprocity. But, beyond the Andes, and its traditional cultural center, this was new and alien, which made the customary method of expansion unsustainable, and as the wars at the ends of the empire show, really, really difficult to achieve.
The only two ways I see for the OP (survival-wise) to achieve its purpose are:
1) Have Ninan Quyuchi survive. (He was the designated heir, but his death shortly before his father’s caused the meltdown.) With Ninan Quyuchi, things continue as always, and you skip the civil war. The plague will come and take its toll, but the state and its infrastructure will stand on better footing. Let’s say that Pizarro arrives with his small band. The aid provided to him from the get-go IOTL will not be present, as the feuds between populations from the civil war will never have happened. If he does land, the Inca will never allow him to come to Cusco, and in fact might not go out of his way to meet them personally; but send someone else instead. Without the Ninan’s security compromised, things might turn ugly for the Spaniards.
If survivors don’t make it back to Panama, it would be a while before more Spaniards attempt anything; at least 10-15 years, during which the Incas can get better acquainted with whatever technology they can get their hands on. Once the Europeans return, you can repeat the same steps; but at some point they might get a foothold, or advance from the north via modern Colombia, which in itself would give the Incas more time to adapt, as they travel though the jungle, hostile smaller tribes, etc.
2) Have Atawalpa die during the wars in the North, while Wayna Qhapak is still alive. (This almost happened IOTL, during a combat in which Atawalpa even lost an ear.) Then you end up with Waskar, who was a detested nut, and would probably end up worse for the Incas, as he would piss A LOT of people off with his shenanigans, turning them into potential allies for Pizarro. But even then, there was no civil war, manpower is greater, and should Waskar be smart about it, he might try to seize the invaders, after which things would turn in a similar way to the first option, but with a lot more popular resentment around.