By this point Lee has already committed his reserves to this sector, which he did about 0800. McLaws, Anderson and Walker are already
en route and at 0920 McLaws and Walker are hitting Sedgwick in the flank.
Lee's decision was made at 0800. This is about the same time as McClellan sent an order to Burnside. Unless there is a missing order (i.e. a pre-0700 attack order) then Walker would still have been sent to the rebel left, along with McLaws and Anderson.
At 0830 McClellan sent orders to Hooker and Sumner, the latter now formed up with the two 2nd Corps divisions in/ by the Miller Woods (tracking the movements of these two divisions I found they were both formed up at the Miller Woods by 2030, significantly in advance of where Carman's map places them).
"Gen[eral] Hooker appears to be driving the enemy rapidly. If he does not require your assistance on his right, please push left through the ravine at the head of which house was burned this morning, getting possession of the woods to the right as soon as possible & push on towards Sharpsburg. Use your artillery freely." 0830 orders to Sumner
"Gen[era]l Sumner has been directed (if you do not require him to assist you on the right) to move up on your left and push forward toward Sharpsburg. P.S. Keep the Genl. fully posted by means of his aides." - 0830 orders to Hooker
These orders kick off the next phase of the battle. McClellan defines the right as Hooker's TAOR (Tactical Area of Responsibility). McClellan has ordered Sumner's 4 divisions (minus any detached to aid Hooker) to drive through the sunken road position towards Sharpsburg, getting possession of the Dunker Church plateau as soon as possible.
McClellan told Hooker to keep sending him SitReps because Hooker was failing to do so, and McClellan was working on partial information. After the Seven Days McClellan had had to reiterate that all corps commanders in battle were obliged to sending reports every 30 minutes, because the corps commanders tended to get absorbed in their own actions. The same thing happened at Antietam it appears.
We of course know what Sumner did in response to this order. What McClellan's picture and intent was seems to be:
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