Actually, you are not as far behind as you think. You are slightly behind in the North, behind a bit in the Center and ahead in the South. Consider Odessa did not even come under siege until August and did not fall until October I think. The Uman pocket was not until August either and you already have control of that area.
A 4 panzer army thrust someplace.. wow. Interesting concept, but I think it has far more draw backs than pluses. Consider some of the following issues:
Logistics: Lets say they go nuts and advance like crazy. They will get so far from the rail heads, they will be screwed.
Can you pick someplace that he would stay and fight? Also take into consideration with the current city fighting vs motorized/mechanized stuff that your armor will have a hard time cracking any well defended cities. You would have to cut them off and starve them out.
Even if you took a huge chunk of territory like that, would you be able to hold it through the winter months? The answer is likely no.
With all your eggs in one sector of the front, the Soviets would be tempted to take risks and try to stop your other advances since they know it is extremely difficult to pull off encirclements without motorized units, especially in the more rough terrain up north. Any Soviet is lying if they don't tell you the first thing they check for is where the Axis armor is. They are scared of your armor and they should be. Having your armor in several positions across the front makes him worry about encirclements in a lot of places, which helps you.
Now, as far as a overall campaign goal, that is tough since you should have probably thought of that before you started your attack..

However..
First off, any plan you may have must also include the destruction of as many Soviet units as possible with higher priority given to his more mobile units, be the motorized stuff or cav. The more you kill now, especially cav, the better off you will be. The second part of any plan must be concerned with preservation of your force. The Russians can't win if your army stays in fairly good shape. After that, setting campaign goals and then working towards them is good; making adjustments as the situation demands. You have already pretty much decided against a campaign against Leningrad, which is certainly an option and given how things are now with the game, probably a good idea. Leningrad is one of those objectives that you have to set even before the first tank crosses the border and its too late for that. Since you have decided not to press Leningrad, you now have to figure out where you will stop advancing in that area and just how many troops you are going to send packing elsewhere. I would also look to make AGN's rail repair unit available for wherever you make your main effort in order to try to advance your rail head that much faster. It is not as efficient as if they all worked independently of each other, but you can advance one line faster that way.
While I think Second Army will help down south, it will not really help press their speed of advance because it is infantry and infantry are going to move only so fast. If you are looking to blitz the Crimea (again, may be too late, but maybe not), then you need some armor in the area. It would not take a lot (probably 1 panzer corps of 3 units) but they need to move down there stat and get out ahead of the infantry so it can advance at a higher rate. You won't do much of anything until the infantry gets to a line to break it in most cases. I don't think any serious attempt to crack the Crimea can be made until your infantry shows up and that is gonna take a bit.
Something to keep handy as well is something I found out about while discussing the weather zones, etc and that is there is a good amount of hexes down south that while they have blizzard conditions, the Axis do not suffer under the special 1941 blizzard rules. Not saying you can go nuts down here like its clear or snow, but you won't be a weakling either and may well surprise a Soviet expecting the Axis to curl up in the fetal position because of the blizzard. The big thing to set this up is rail heads have to be well advanced and that appears to be very, very tough in the south, but who knows..
Sorry for the book, but this is a great looking AAR and you did ask for opinions.. [:D]