However, he could not. The appointment of corps commanders was a Presidential power, and their removal required the exercise of Presidential power. Sometimes the President might seek advice before making the appointment, but it was solely their prerogative. Grant had to manoeuvre Smith and Burnside out of position, he couldn't simply reassign them.
If he had wanted to get it done before the start of the campaign, he would have gone through the usual procedures. If he needed to do it on the field of battle, he would have simply ordered it done and dealt with the consequences later -- as he did with Warren. Warren wasn't cashiered or stripped of rank, simply removed from command of his Corps and reassigned to a similar position. But as mentioned in a post above, we should not turn this thread into a digression about Warren and Sheridan.
In early 1864, Grant actually had a good impression of Warren and considered him as a potential replacement for Meade if he needed Meade to go. He had never met Meade before, IIRR, and was unsure how that relationship would work out until he went to meet him after coming to Washington. Sedgwick was regarded as a good, solid soldier -- but I don't think anyone was pushing him as a tactical genius or the next great independent commander. Burnside had a lot of baggage and I would think Grant (particularly after the Knoxville experience) wanted someone else -- but Grant was aware of the political issues with men like Burnside, Butler, Hunter and Sigel. That's why he did not push to replace them before the campaign started.
As to who might have replaced those people, Grant had his own ideas. When he came East, he wanted to bring back some of the sidelined talent, men like McClellan, Buell and Franklin. The first two didn't get go anywhere, although McClellan's name was still floating for a command in July, 1864. Franklin was Grant's first choice for the AoP Cavalry, but there was too much resistance, leading to Sheridan's sudden advancement with Grant's classmate Franklin going to serve under Banks (Sabine Pass fiasco and Red River Campaign, wounded at Mansfield, replaced after Pleasant Hill as his condition deteriorated).
I can't believe either Buell or McClellan would have come back for anything less than an important independent command, although both had the skill and ability to be very useful to the Union if they would put their heart into it. Neither looks like they would be a fit for the Lincoln administration, particularly with Stanton. But Buell surely would have been an interesting replacement for Butler or Banks that Spring, and how different would things have been if Grant had managed to bring McClellan in to replace Halleck as a fantasy?
Sherman might have been an interesting choice to replace Meade, perhaps with Meade going to replace Sherman or with Thomas taking Sherman's spot. If Meade, Sherman and Thomas were to stay where they were and Burnside was somehow eased out, here's a big change: McPherson comes East to take IX Corps. Maybe Sigel gets eased out and McPherson gets the Shenandoah. Grant and Sherman both thought McPherson was a rising star.
Overall, I think Butler, Sigel, Burnside and Hunter were the biggest command problems in the East for Grant. From a military standpoint, Burnside may actually have been a lesser problem than Butler and Sigel (because he was where Grant could exert personal control over him in a crisis). Grant's early 1864 plan relies on Butler and Sigel in positions they could not handle. Sigel's failure can be seen as minor in some ways, but without Breckenridge's reinforcement to Lee, Grant probably turns Lee's flank and might have taken Richmond, with the whole Cold Harbor disaster being avoided, in early June. Just a little more success from Butler against Beauregard in May might have forced Lee to retreat from Spotsylvania and back to the Richmond defenses. Replacing Burnside might mke a battlefield difference along the way in May or June, but I can't see a clear case for it giving Grant a smashing victory.