From the sound of it (3 missile posts close together, under the same shields, if I understood correctly) that's a subcommander planet. Thankfully, most planerts in the game don't have one of those
They can be tough nuts to crack.
There are a bunch of bonus types that would make that a lot easier if you had them (shield bearers, zenith devastators, youngling weasels, protector starships, etc), but you might not have any of those. Though if the
AI has a type you think would cut this knot, you could hack to copy that type (which is possibly a better deal than sabotage would be here, as it wouldn't be purely a one-time benefit).
In terms of always-available stuff I think most of it has been mentioned. Transports, in particular, make any kind of assault more likely to survive, though bear in mind that ships exiting a transport have to reload from empty before firing.
Assault Transports, on the other hand, leave the ships at half-reloaded status when they exit (assuming they were at least half-reloaded when they entered), which improves the post-unload alpha. Also, the assault transports themselves have some non-trivial firepower when fully loaded, so you could just stuff your full triangle fleet into those and have them sit on top of the offending post/shield cluster until the transports died and let the little guys out. My guess is that this would be a tenable form of whittling, if not particularly efficient.
Mobile Space Docks are potential options for whittling, as they can just keep cranking out the ships (possibly from fairly close, thanks to their radar dampening iirc) so as to make attrition warfare more viable. There's also the Enclave Starships for throwing out extra chaff to clog targeting lists. One thing in your favor is that a Missile Guard Post's rate of fire is pretty low (compared to an MLRS, for example), so just zerg-swarming it is more viable than it is with other things.
Higher-mark raid starships have already been mentioned, but I'm not sure if anyone mentioned Scout Starship IVs which actually provide missile immunity tp all nearby allied units. That may be more K than you want to spend on this
And yea, any time you see big shield clusters (or anything nasty under shields, really), consider the plasma-siege starship. Particularly if you have other stuff drawing fire so they don't die fast (attrition tactics with starships get, um, expensive), they can take out a lot of stuff "under glass" or at least contribute to the doing so.
In summary, there's a lot of things you
could do. Figuring out what's the right balance of cost and effectiveness is the challenge
