In looking at the possibilities of that plan, I think the really tricky thing is what has to be achieved to establish supply. This is because Grant has three possible ways to reconnect with supply after his movement:
1) Reconnect with the Orange and Alexandria
This involves clearing the rail line from Culpeper down to wherever it is he reconnects with the rail line, such as Gordonsville or Charlottesville, as he can then recieve rail supply there. The main risk here is that he needs that whole rail line to be intact, or as far south as possible, to make it function - if he marches the sixty miles around the headwaters of the Rapidan from Culpeper to Charlottesville, only to discover that Lee has wrecked the rail line through Culpeper county and Charlottesville is 50-60 miles from his rail head, then Grant has no real succor except to march straight back.
This means that Grant can't send his whole force on the outflanking move. He has to defend the rail line through Culpeper, and that will cut down on the force he can send on his flanking move (plus it offers the possibility of Lee defeating him in detail).
This is not insurmountable but it is a possible issue.
2) Get to Fredericksburg/Port Royal and connect to supply there.
This is a long march (I make it ca. 90 miles to Fredericksburg if going around the headwaters of the Rapidan) and it has the same problem as the move through the Wilderness - all Lee has to do is delay Grant for a few days and the prospects of the move get worse over time as the food runs out. Lee can quite readily present a front of two corps which is hard enough that it takes most of a day to deploy the forces to overcome it (down two roads) and every deployment takes time which slows Grant's movement; Grant's "exit route" through Culpeper is his abort button if the campaign goes badly, but this is as vulnerable as in (1) to Lee wrecking the rail line and would need to be defended if Grant wanted to keep that option open.
3) Get to Richmond/the James area.
This is the longest march of all. It's 160-170 miles going via Charlottesville to get to either White House Landing (the head of navigation on the Pamunkey) or Bermuda Hundred, possibly more in the latter case depending on how far upriver you want to cross the James, and at that point you really do need to rely on foraging en route which means dispersal.
It just seems to have the same basic problems as the Wilderness route in all cases (time limit before you regain supply) but with the time limit being stricter and a serious risk of losing your "escape route" (in (1) and (2)) unless you divide your forces.
On April 9th, 1864 Grant is at Culpepper C.H., writing his thoughts on the coming Spring campaigns to George Meade. After the parts about Sherman and others, he gets to Meade and the Army of the Potomac:
Lee's army will be your objective point. Wherever Lee goes, there you will go also. The only point upon which I am now in doubt is, whether it will be better to cross the Rapidan above or below him. Each plan presents great advantages over the other with corresponding objections. By crossing above, Lee is cut off from all chance of ignoring Richmond and going north on a raid. But if we take this route, all we do must be done whilst the rations we start with hold out. We separate from Butler so that he cannot be directed how to co-operate. By the other route Brandy Station can be used as a base of supplies until another is secured on the York or James rivers.
These advantages and objections I will talk over with you more fully than I can write them.
Burnside with a force of probably 25,000 men will reinforce you. Immediately upon his arrival, which will be shortly after the 20th inst., I will give him the defence of the road from Bull Run as far south as we wish to hold it. This will enable you to collect all your strength about Brandy Station and to the front. There will be naval co-operation on the James River, and transports and ferries will be provided so that should Lee fall back into his intrenchments at Richmond, Butler's force and yours will be a unit, or at least can be made to act as such. What I would direct then, is that you commence at once reducing baggage to the very lowest possible standard. Two wagons to a regiment of five hundred men is the greatest number that should be allowed, for all baggage, exclusive of subsistence stores and ordnance stores. One wagon to brigade and one to division headquarters is sufficient and about two to corps headquarters.
Should by Lee's right flank be our route, you will want to make arrangements for having supplies of all sorts promptly forwarded to White House on the Pamunkey. Your estimates for this contingency should be made at once. If not wanted there, there is every probability they will be wanted on the James River or elsewhere.
If Lee's left is turned, large provision will have to be made for ordnance stores. I would say not much short of five hundred rounds of infantry ammunition would do. By the other, half the amount would be sufficient.
In his memoirs, Grant says that the supply issues decided which approach they would take:
At this time I was not entirely decided as to whether I should move the Army of the Potomac by the right flank of the enemy, or by his left. Each plan presented advantages. If by his right–my left–the Potomac, Chesapeake Bay and tributaries would furnish us an easy hauling distance of every position the army could occupy from the Rapidan to the James River. But Lee could, if he chose, detach or move his whole army north on a line rather interior to the one I would have to take in following. A movement by his left–our right–would obviate this; but all that was done would have to be done with the supplies and ammunition we started with. All idea of adopting this latter plan was abandoned when the limited quantity of supplies possible to take with us was considered. The country over which we would have to pass was so exhausted of all food or forage that we would be obliged to carry everything with us.
However, later in his memoirs, making comments on what he thought after it was all over, Grant said that if he had experience with the Army of the Potomac before that campaign, had known how good an army it was, he would have been inclined to try his first impulse, to turn Lee's left. That is certainly a risky plan.
On your three options, I can tell you that Grant would have done everything he could to avoid #1. He had a personal trait of hating to re-trace his steps. He would go to great lengths to find another way (including walking completely around the block instead of just turning around to get to his destination).
My guess would be that Grant would have assumed some form of #2. He clearly had given thought to uniting Meade's force with Butler's back in early April, and he was attempting it with Sheridan's raid in May., does it again at the beginning of
May June at Cold Harbor, then crosses the James to Petersburg. If he was thinking in terms of your #3, I would guess he would have done it in more than one step.
Any attempt on Lee's left creates difficulties on supply -- but decreases the chance Lee will break free and head North.
Any attempt on Lee's right eases difficulties on supply -- but increases the chance Lee will break free and head North.