In the end, my solution was to do some initial analysis of the problem, which allowed me to be very confident that there were many less pythagorean triples than there were possible triples summing to 1000. Thus, I started by generating the pythagorean triples in a reasonable range that I figured would contain the solution. After that, I extracted the triples from that and reduced them to only the one combinations that add up to 1000. This will give only a single set of triples, but two different results in two orderings.
This is an especially inefficient operation memory-wise, because it is computing way too many results. On the other hand, for what it is doing, it generates these triples and filters them plenty quick enough.
R←PENINE;X;Y;I;⎕IO ⎕IO←1 ⍝ Product of the pythagorean triple where a + b + c = 1000. X←500 ⋄ Y←(⍳X)*2 Y←Y∘.=Y∘.+Y I←1+(⍴Y)⊤(,Y)/0,⍳(×/⍴Y)-1 R←×⌿1↑(1000=+⌿I)/I