So lets consider lvl30+ bosses (or whatever the cutoff is for reds) and 2 soulseekers.
The new chance to get a soul would be (1+0.35^1+0.35^2)*0.05 = 0.073625 = 7.36%
Then the new chance to get a red would be 0.073625*0.05 = 0.00368125 = 0.37% (1 in 400 --> 1 in 270)
Something like this:
If you're hunting red souls specifically, it's best to speedrun Foothills in 3-man cells with 3 soulseekers. Even if you're in a party, the 5th and 6th soulseeker isn't even noticeable.
So are multiple soulseekers useful? Yes, up to 3, maybe 4. Is it viable to now grind for red souls if you have soulseekers? No.
Your logic is better but our formulae are still off I think. Any which way, the chance increases well for 2-3 soulseekers then drops off severely and overall the chance is still minuscule.
I don't know about solo farming, since reds don't drop in D2 anymore. Sure you can solo foothills a bit but it's quicker to do the full rotation with 2-3 players than just wait for HG to respawn. Right? I guess it's up to preference, but I wouldn't bother either way. It took an absurd amount of time even back when Protector reds were a thing, unless you're speedhacking (read "cheating").
SHBlade has the correct formula. This is also how the bard talent and Yarr bonus works.
Also, remember that the random dungeon does drop red souls from treasure chests and bosses.
The chance for getting a red soul drop from chests and bosses rises exponentially with every new floor in Blackfire Deep.
And also remember: the chance to spawn a chest or boss also rises the deeper you go, so overall, you will eventually hit a point at which you almost get a guaranteed red soul drop on every floor.
The chance to get a red soul drop from a treasure chest in Blackfire Deep is roughly 1.5% on the first floor and rises up to a whopping 33% on floor 50.
This is why getting a Keystone is key (no pun intended) and probably much better than farming foothills bosses all day long. The blue quality keystone will grant you instant access to floor 20. At this floor, the chance to get a treasure chest is twice as high as on the first floor - and the chance to get a red soul drop from these chests is also already at ~4%.
As you can take souls outside no matter if you die or not, it's pretty much a no-risk scenario, if all you care about is getting red souls.