But it might still prove that we should agree to make more people and more resources if it's a package deal.

It does, but by definition.

Let X and Y be populations. Each population has a number of people and an amount of resources. Resources are distributed evenly, so the average utility of a population and each individual's utility is given by: resources over people. We will say the "standard of living", the level at which a life is 'barely worth living', is a utility of 1. And we will say that Z is when the utility is below the standard of living. These are our definitions.

For numbers, let's say X and Y start out with 100 people and 500 resources, giving each a utility of 5. This is good!
In X, we will perform the false method: simply adding people. In one step, we go to 105 people (utility 4.7, still good), then 110 (utility 4.5) and in 80 steps we will have reached our repugnant Z, with 505 people and 500 resources giving us a utility of 0.99.
Now in Y, we will perform the strengthened method: absorb a small population with bare minimum living standards, thus bringing everyone down slightly. In one step, we got to 105 people and 505 resources (4.8 utility, still good) then 110 and 510 (4.6, still good) and then Z arrives ....

No, it doesn't. Utility in Y will asymptotically approach 1 from above and we will never reach Z. Thus, the repugnant conclusion is dead.

You may argue that "just barely above the absolute bare minimum" is not worth living, but you won't get very far: previously, we defined any life above the minimum standard as worth living. So if you say that, instead, 2 utility is the minimum worth living for, Y will asymptotically approach 2. And you can hardly argue that "just above 2" isn't worth living for, because you just said before that 2 is the minimum! So yes, the repugnant conclusion is truly dead.

(An analogy for this population Y is colonising new planets: the older planets will be affluent, but the frontier new colonies will be hardscrabble and just barely worth it. But this is not a repugnant conclusion! This is like Firefly, and that would be badass!)

Or you may argue that comparing our original Y to a Y++ after many steps, it's obvious that Y is better. But this won't get you far either, because in what way is Y better than Y++? If you tell me this comparison beforehand, I will no longer desire to add people when it would reverse that comparison, and if you don't tell me, well, that's unfair - it's no surprise that optimising for one criterion might abandon other criteria, especially ones it didn't know about.

Footnote:
I tried this:

b = 500
a = 100
while (b / a) > 1
b += 5
a += 5
end

and it didn't terminate, thus the student became enlightened.