You're better off re-routing the feeder to the new box, and then running power to the original box as a subpanel.
The reason is subfeed lugs are costly or unavailable. The only panels that come with them only have 4-12 spaces. So you'd need to buy one that mounts in breaker spaces, and they're not even made for most panels, and very expensive for the panels they are made for. Note that it is not safe to cross brands of breaker, so don't go thinking a Square D "HOM" subfeed lug kit will be your solution for a GE or BR panel that doesn't offer them.
So what do you do instead? Use a regular breaker to feed the old main panel. Something like a 60A breaker (because it's cheap) using 2-2-2-4 aluminum, 4-4-4-6 aluminum or 6-6-6-6 copper SER if the distance is short (because it's cheap). That gets the connection done for $30-50 without the need for costly subfeed lugs.
You may notice 60 < 200. That's true. The fact is, very few of your loads take the vast majority of the power. So relocate 2-3 of your largest loads to the new panel immediately. That's not a lot of work. This time of year I would move over A/C, and water heater. I'd focus on automatic loads you can't control. Most likely, you won't have a problem powering the rest of the house off 60A at this point especially if you are cautious. If you do have a problem, go ahead and move over dryer and range too. And I gather you're not using heaters much this time of year.
All the 120V loads in the house are vanishingly unlikely to trip a 60A breaker. Houses just don't use that much power (other than the 240V loads).