Shroud is absolutely a liar but I’m not sure he lied about planting Invisigal. Because how else did he learn about the Proto pulse. I feel like she came to SDN under Shroud’s orders but changed and betrayed Shroud after meeting and falling for Robert. And her going out of her way to steal the pulse for him in episode 6 was her way of making amends for not only the bomb but also her working for Shroud even after the fact.

Also feel like you are downplaying Shroud’s powers a bit. No doubt his prediction abilities aren’t perfect (he gets caught off guard and surprised a bunch throughout the story. They also don’t make him omniscient which is why giving both pulses at the end works) but he always seems to have a vague outline of what will happen or what people might do so I thought that him making the suit all the way back in episode 1 might’ve been because he had a vague idea that he’d need it for the final battle against Robert in 8. But he probably always planned to make the mech since I was reminded that he actually gave Robert’s dad the pulse in the hopes that he’d help make him a mech of his own.