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The Doctor doesn't allow himself to believe until it's over, but he won't accept that his plan won't work either. He lets expectations hang in a quantum state, afraid of having his hopes crushed, not willing to admit that his nearly impossible plan might not work.
The TARDIS can't land on another dimension, not without contaminating her power supplies and getting stranded, so he could do it and hope that he has another idea to fuel her later, but that's a big gambit, depending on there being a compatible power source in an empty dimension, or something that can be adapted as such. But if his calculations are right, and he's had the TARDIS checking and rechecking them so they have to be, the dimension that he's trying to reach is just a little to the side, at a neighbouring wavelength, just close enough to do something risky and reckless.
“Come on, honey, you can do this, I know you can,” he says, kissing the console as he holds down the lever, holding them at the edge of materialisation, with impossible coordinates and settings that won't allow them out of the vortex, not all the way.
The TARDIS screeches and shakes like she might fall apart, sparks and flames jumping from the console, but he holds on, grinding his teeth as he feels himself and the TARDIS vibrating almost out of phase, but then he sees it, the shadow of a form laying on the floor on the other side of the console, and he knows it's working, she just needs a little more power.
He keeps holding down the lever as he adjusts the controls, trying to give her everything he can. This is so close to working, they just have to get a little closer to materialisation, just a little…
The explosion pushes him back, and he hits the doors, too far away to do anything when the TARDIS dematerialises again, tossing herself to the vortex and away from that dimension's indigestible energy. He rushes past the console, levers and switches shifting by themselves as the TARDIS deals with the fire and returns to a sustainable setting, but he needs to know if it worked.
“Rogue,” he says as he practically tosses himself on the floor, reaching the body laying immobile there. “Please, darling, I need you to wake up, please tell me it's not too late.”
He tried to get as close to when Rogue arrived as possible, but he couldn't aim for a small window of time, not while also aiming for a precise point in space. They couldn't materialise fully, only bump the other dimension and leave, almost materialising around Rogue so when they pulled back he would be dragged along when they slingshot back. He doesn't know when they reached him, he doesn't even know if Rogue could…
Rogue coughs, bending over, and the Doctor holds him, trying to offer some support. Coughing is good, coughing means breathing, breathing means it's not too late.
“Doctor?” he asks, looking up, blinking and squinting his eyes against the light.
The Doctor didn't allow himself to think of what might happen, it had to work, but he didn't know if it would, and he couldn't let himself think of any next step. So it takes him as a shock, not that his plan worked, but that it worked, not the slingshot from another dimension, but having Rogue back. Rogue is alive and safe and with him, and the Doctor didn't think of a single thing to do if that happened.
The Doctor pulls him to his arms, holding him tightly like he's afraid that Rogue might disappear if he lets go. Rogue holds him just as tightly, his fingers digging almost painfully on his back. He feels the tears stinging in his eyes, and doesn't try to fight them. Rogue's here, he's safe, his plan worked.
“I knew you'd come, I knew you'd save me,” Rogue says, his voice muffled on the Doctor's shoulder.
“I'm sorry it took so long, I was trying to find you, I'm sorry I couldn't be faster,” the Doctor says, kissing Rogue on the side of the head, then pulling him back just enough that he can trail kisses until he reaches his mouth.
The Doctor kisses him with a tenderness that doesn't betray his urgency, unsure if he's comforting Rogue or himself. He can make up for the time this took later. All that matters now is that it worked, they're together again, and Rogue is safe. If the Doctor tells himself that enough, he might start to believe it.