I ran this scenario for 100,000 hands. The raw results showed an EV for S1/S3 of +0.681 for passing and +0.683 for bidding - so virtually identical.
Looking more closely at how the hands were played when S3 bid, I saw many plays which were debatable and perhaps not optimal. But impossible to say without doing extensive testing of various scenarios for a plethora of hands. Just too time consuming for a relatively rare scenario. While I do want to optimize my program, I am looking more for the obvious errors - the "low-hanging fruit", as it were.
So at this point I would just conclude that it's a toss-up whether it's better to bid or pass this hand from S3, R1. What's much more important is the quality of your - and partner's - play.
All that said, I then ran a simulation for 100,000 hands to test what S3 should play after a trump lead by S1 on the first trick. 1st scenario is that S3 always plays the R. 2nd scenario is that S3 will play the 9C if S1 led the KC, otherwise will play the AC. [S3 will always play the 9C if S1 leads L]
1) [play R]: (9,919 / 49,482 / 4,191) [2 pts / 1 pt / euchred] EV = +0.96
2) [play AC]: (10,471 / 47,213 / 5,908) EV = +0.89
So I find that playing the R in this case is better. It leads to fewer 2 pt wins, but also far fewer euchres. That said, although my results are statistically significant, they do still rely on correct play of the hand by my program. I find this to be a complicated hand to play out, so I can't guarantee my program plays everything correctly. But the mistakes are also equally likely to be on offense as on defense. I would opt to play the R after seeing these results. Why? I find it important to be able to explain the results I arrive at, and not simply blindly follow them.
So what is going on with this hand? S3 has 3 trump, S1 has at least 1 trump [we are looking at the scenario where they lead trump, 1st trick], and S4 has at least 1 trump [picked up by dealer]. So 2 more trump out there, including L [in this
particular hand, S2 followed suit, and so accounted for the 6th trump, but I am assuming a more general case]. If S2 has the guarded L, it would be best to play the AC from S3 - but this is a very rare case [one particular seat has both the unaccounted for trump]. If S4 has 3 trump [can't be true in this
particular hand, as S2 followed suit, but can be true in the more general scenario I tested], things look dire for friends in S1/S3. But this, again, is a very rare case.
[I will also assume that S1 doesn't have a 2nd trump, as this would be an equally rare case.]
So most likely, L is either buried or sits with S4. If it's buried, S3 has 2 boss trump and is almost assured of making a point; the uncertainty of where it lies (and subsequent decisions on how to play) may explain the difference in 2pt wins. What appears critical here is the case where S4 has 2 trump and guarded L, which happens to also be this particular case.
To euchre S1/S3, the opponents need 3 tricks. Say S3 wins the 1st trick with the R, S4 plays their low trump (QC), and S3 leads a low D. S2/S4 can euchre if they have 2 boss Diamonds (and coordinate their play appropriately), otherwise it's a bit up in the air. If S3 plays the AC on the 1st trick and lets S4 win with the L, S2/S4 can win a 2nd trick with a D lead (if they have the boss card - and even possibly a 3rd), but also set up S4 to have the choice of over-trumping S3 on a later trick, or playing off, saving their trump for later. I thinks it's this flexibility - having a trump and playing
after the strong opponent - that gives S4 the edge.
My reasoning may be flawed - I'm sure Irish will let me know if it is

! And by the way, regarding the "rare" cases, one favors S1/S2, one favors S2/S4, and the 3rd is just dire for S1/S3 either way - so a wash.