If it's not a boarding mission to discover what's there, just send a bunch of drones with meson nukes in their backpacks.
The GTDr Amazon is referred to as "not smart", so I assume there is AI in universe that can control a machine much better.
Stealth is also very effective vs the Shivans, I guess using a normal Hecate loaded up with stealth strike craft to try to disarm or disable a Sathanas before the main strike could be a big force multiplier.

I know this is a non-canon ship (GTF Icarus), but hey, we're speculating here. It can equip the Trebuchet and the Maxim, and the Sathanas's main beams were not exactly heavily armored.
The Pegasus can load the Trebuchet and Akheton as well if we'd assume this fighter would not be ready in the numbers needed for these operations.
On a side note - I did not find a single stealth bomber in the FS wiki... 
Can anyone maybe mod the Icarus to be a bit beefier? I can supply sketches of how I see it to be... 
Another strategy with the GTVA superior strike craft is standoff weapons.

This ship (GVB Setep) is described as able to carry subspace strike torpedoes, so one can imagine stealth fighters in the initial raid to hopefully disarm a Sathanas and to say hello to the enemy fighters, followed by a bunch of conventional ships to do the heavy dogfights and then the third wave would be these bombers, tossing torpedoes that would teleport to be close to the target while these bombers stay away from most trouble.
Don't know how much a subspace drive can be miniaturized and how many such torpedoes a bomber could realistically carry though. Mods do not define canon too much. 
Ya know? THat sounds like a great Idea for an alternate history confrontation with the Sathanas fleet: it's a one way trip (Al la the IJN Yamato in 1945) and you're gonna get blown to heck but, lets see how many we can take with us. Either choose the Colossus or an upgunned destroyer, jump in as they gather at the Capella sun and just 'go to town' (or if you're feeling like a cheat you can include the Erebus destroyer and/or some of Herkie's super ships ;RIP brother).
"How many we can take with us" is zero. A redlining Colossus took 15-20 minutes to destroy a Sathanas. It takes about 60 seconds for a Sathanas to destroy a Colossus. Anything destroyer sized or below is history in two salvos or less.
Even a destroyer ramming into the Colossus, which has the exact same number of hit points as a Sathanas, caused minimal damage.
The aimable Mjolnir is a bit more powerful than the Colossus's 20 year old tech when supercharged. The Mjolnir set to fire along the beam emitter's axis is about 2x that.
The upgraded Hecate (GTD Icelus) could also benefit from the tech that made the Mjolnir beam and just have two of those on its nose mounts - so firing both down the axis gives more than half of a Colossus broadside, and it's not like one cannot aim a destroyer at a juggernaut.
This again shows how far behind the Big C became during its development.
Would still want the Vasudan Crossbow though. Vasudans are known to have significantly stronger beam cannons than Terrans... and with a beam cannon that big I'd think it would match or exceed the dual Mjolnir Icelus.
Then it's just a systemic planned battle till the Shivans figure it out (and they seemed to be not very adaptive planners).
P.S. Found this in like 2 seconds of searching:
https://www.youtube.com/watch?v=gcWhhsRGsAI
You can strap an engine on a Meson Bomb, but then you've just invented a very large slow missile.
Stealth bombers, I'm not sure they're even feasible. Bombers have a lot of mass and FreeSpace engagements are in visual range.
Trebuchets barely scratch the Sathanas' frontal beams.
I don't think you can necessarily just plug in a Mjolnir#Home on the front of your destroyer. Presumably all those arms on the Mjolnir perform some important function and it's the size of a small cruiser. Even if you could, even if you got 5 of them pointed at a single Sathanas, the Mjolnirbeam does 1,257 damage per second, so 6,285 for 5 of them. The Sathanas has 1,000,000 hit points. So you're looking at 160 seconds to take it out. Its 4 front beams do 32,340 damage per second, your toughest destoyer, the Hatshepsut, has 135,000 hitpoints.
But you're not worried about that, you go to the rear, right? The LRed on the rear of the Sathanas puts out 2,100 damage per second, it will have destroyed your toughest destroyer inside of a minute.
By the way, they also have jump drives, so if you're winning they can either leave, or use one of the other 80 Juggernauts they've got in the system to show up and obliterate you in 5 seconds. And they can deploy lots of fighters themselves.
Any efforts to go after them is a suicide mission with no upside.
If we're dealing with a single Sathanas, how about jumping in from the side to avoid it's main beams? Okay... The attacking ships would have to be fast enough to keep up with it's rotation speed...
But yeah, taking front beams out is the best strategy.
And like mentioned in this thread before: Commands hubris just is hillarious. I've re-played FS2 campaign recently (haven't played it for quite some time) and I really had to wonder about the mantal state of command...
Hey, there's a new portal to an unknown nebula with many shivans in it and with very limited sensor range. Let's not just guard the entrance, but poke at the hornets nest as much as possible... We had 30 years and are now SOOO much better than shivans...
Oh noes... Ravana! We lost many big ships... Alpha, take bombers and save us! Oh, we're saved... That shows our technical superiority!
Let's resume poking the hornets nest...
Oh noes... Sathanas... Lost capships in seconds... Closing portal failed... Alpha help us! Take bombers and disable main waponry! Woohoo... Colossus took out sathanas after oh-so-many minutes while melting all it's electronics in the process (according to comms in mission). We are soooo superior. So let's continue poking at hornets nest!
And, oh... There's another portal! Let's see if we can go through... Oh noes... MANY Sathanasesesesesesesesesesessssss....
And the colossus' brain has melted in the attack too... Trying to "hold off ONE Sathanas as long as they can"... I don't think those ten seconds mattered that much...
It's not communicated very well, but I think the issue with the Colossus was where it goes if it jumps out, given that the Sathanas might follow it.
If it goes to the Epilson Pegasi node and the Sathanas follows it then the Bastion could get caught in the crossfire and the whole plan to seal the Shivans off is doomed.
The Vega node is where all the refugees are fleeing to/through.