This is just completely wrong. You only need one side to be in motion to have a "meeting engagement". The other side can be in the Maginot Line and invisible. They can be hiding in the bushes waiting to come out and ambush you. Or they can be galloping down the road in an all-out charge to run you down. It doesn't matter, you are still in a "meeting engagement".
By that definition literally every battle is a meeting engagement except for those during positional warfare, and thus the term is unhelpful. If the same definition describes Antietam, the Charge of the Light Brigade, the Battle of Gettysburg, the Schlieffen Plan and Sickelschnitt, then it's too broad.
The definition you're giving is functionally that of
manoeuvre. A meeting engagement is a specific subset of that, which is where neither side "owns" the territory to start with - that's why the Army Manual of Operations discusses how commanders "may choose to establish a hasty defense if the enemy force is larger or the terrain offers a significant benefit."
Clearly this doesn't apply to Yorktown, which is a fortified area and thus the term we should be talking about is either
penetration (an attack on one specific location) or
frontal attack (an attack all along the line).
Another general might have done differently -- a Grant, a Lee, a Jackson, a Sheridan almost surely would have.
But how? Would they have ordered an attack on the 6th? What form would this attack have taken?
What you're doing is repeatedly saying that other generals would have done differently, but repeatedly refusing to specify what form that "other thing" would have taken - and I conjecture that this is because you either do not know
how another general would have succeeded, or that you suspect any specific option will prove impossible.
So let's have a look at those options again. No matter who the other Union commander is, they have to do one of these things.
1) Attack off the march on the 5th, at the locations this took place in reality.
There is no change to what happens. A Grant sending the same orders to the same people cannot make them more inclined to charge artillery.
2) Attack off the march on the 5th, with one wing attacking past Garrow's Chimney.
This does require hindsight, but it might work. It involves taking the advanced work south of the river (if defended), and attacking with multiple brigades in delayed succession across the river. Owing to the nature of the ground they don't actually know whether the river's fordable until they reach it, and what you'll end up with is large numbers of troops being fired upon by many guns (over a dozen) as they struggle across neck-deep water. They will each have one shot in their rifles if they hold them over their heads, and their cartridge pouches will be soaked. Against them you have one large brigade (a good few thousand effectives) who have works and dry powder.
If these men then make a successful bayonet charge, congratulations, the crossing's cleared and you can cross troops able to actually continue to fire their weapons. But since nobody knew about this crossing point and no major roads lead there, it's not really very likely - most successful bayonet charges involved setting up a base of fire first, and Civil War infantry are not good at closing with the bayonet against works.
3) Form troops and attack in the afternoon of the 5th, at:
a) Lees Mill.
With perhaps two divisions trying to file across a narrow dam and with all attempts at artillery support being shelled to bits as they deploy, this is going to be very bloody indeed and will probably not work. There's just not enough frontage when crossing.
b) Garrow's Chimney
Same as the above (2), though you can now put troops in as a continuous wave instead of just one brigade at a time. The problems all still exist, however, as you're sending troops to struggle across deep water and then mount bayonet charges against works.
c) Red/White Redoubts
There's only about a thousand infantry in here, but the approach is a nightmare - it involves crossing a mile wide killing area under the fire of as many as a hundred guns, including a long period moving parallel instead of directly at the guns. Even a full infantry division might not make it within small-arms range of the target, there's a truly titanic amount of firepower pointed at them.
d) Yorktown directly.
Again, about a thousand infantry present, but this time you're charging directly at a fortification that can engage with more than sixty guns. It's actually less bad than attacking the R/W Redoubts, in terms of the approach, but the attack itself is harder because Yorktown's got better walls.
4) Make an assault on the 6th.
The same four targets are an option. You have more time to do prep work (such as bringing up batteries) but Magruder's also been reinforced by more troops - for example, Early and Rhodes have arrived, bringing about 5,500 bayonets to reinforce the line.
Note that the option most likely to work involves hindsight - specifically, discovering the crossing discussed earlier on this page, and throwing in a full assault by the entire wing the next day - requires massive hindsight (discovering the Garrow's Chimney approach, guessing that it is a ford sight unseen, and committing to it despite the risk the water is too deep to ford) and is still not very likely to work.
5) Make preparations for a full assault on the 7th.
This would run into the problem of the storm, which made vehicular movement impossible.
6) Conduct a thorough recon and mount a set-piece assault on the weakest point of the line, using skirmishers to protect the engineers as they do their work.
McClellan did this in reality, and if you can (with precognition) prevent the Vermonters from screwing the whole thing up you have a plan - but, of course, if it works then it's going to be because Grant (or whoever) avoids the bad luck that McClellan had.
7) Blast the enemy out.
McClellan decided on this after all other options were exhausted.
8) Have the navy run past and take the redoubts from the rear.
Not possible for McClellan owing to a combination of the physical reality of the batteries covering the York, and Wadsworth.
9) Take Gloucester Point with the amphibious division to make a right turning movement.
Not possible for McClellan owing to Stanton and Lincoln.
10) Make a left turning movement over the Warwick southwest of Lees Mill.
Not possible for McClellan owing to Confederate gunboats.
11) Attack somewhere else along the line.
Not possible for McClellan owing to lack of being Moses.
12) Something else?
If you have a better suggestion, of course, I'm all ears. Absent that, the onus is on you to indicate which you think Grant would have done - after all, it's all very well to say he would have attacked, but there's only a few choices and they're all quite bad. The weak points aren't very weak and any attacks with a single brigade will be repulsed by the dug-in artillery, so probing for the weak point is largely guesswork.