I gave you a numbers so you can do the math and prove us wrong, but alas you have declined to so, I guess it's my turn now.
Fauztinville:
NoDrop = 1197
ProbSum = 1218 (NDgoldX* = 495)
TotalProb = 1197 + 1218 = 2415
Effective chance to drop anything:
p1: 1 - (1197 + 495) / (1197 + 1218) = ~30%
p3: 1 - (396 + 495) / (396 + 1218) = ~45%
p5: 1 - (168 + 495) / (168 + 1218) = ~52%
p7: 1 - (78 + 495) / (78 + 1218) = ~56%
Corrupted Abbey:
NoDrop = 1200
ProbSum = 1113 (NDgoldX* = 431)
TotalProb = 1200 + 1113 = 2313
Effective chance to drop anything:
p1: 1 - (1200 + 431) / (1200 + 1113) = ~29%
p3: 1 - (409 + 431) / (409 + 1113) = ~45%
p5: 1 - (180 + 431) / (180 + 1113) = ~53%
p7: 1 - (86 + 431) / (86 + 1113) = ~57%
Lab T10:
NoDrop = 902
ProbSum = 6098 (NDgoldX* = 3163)
TotalProb = 902 + 6098 = 7000
Effective chance to drop anything:
p1: 1 - (902 + 3163) / (902 + 6098) = ~42%
p3: 1 - (102 + 3163) / (102 + 6098) = ~47%
p5: 1 - (13 + 3163) / (13 + 6098) = ~48%
p7: 1 - (1 + 3163) / (1 + 6098) = ~48%
Where NDgoldX* is a substitute for NoDrop which is not affected by players count.
Where p1/p3/p5/p7 is an equivalent for players command from sp, e.g. for a multiplayer game p3 is the same as having 2 players within the same area in party or having 3 players where each one is farming their own area.
I can clearly see a benefit while playing in party if you want to be efficient with your farm, it's ~15% better chance and that's a substantial bonus, can't argue with that. Now let's take a look at the rest of results, it's ~8% better chance from p3 to p5 and only ~4% better chance from p5 to p7, where is that significant difference you were talking about? Maybe you want to talk about the Dimensional Labyrinth, there is barely any advantage if you're not farming it solo, these numbers are speak for themselves.
From now on it would be better if you use the actual statistical data if you want to resolve this dispute, it doesn't have to be my calculations, you can bring your own.