Laying the new floor in the same direction as the old floor is not the normal way to go about this. In the building industry, it is more common to see layers that are staggered or "bricked". In other words if layer #1 is laid in a North-South direction, then layer #2 (the top layer) is laid perpendicular to it in an East-West presentation.

If you want to run the new flooring in the same direction as the old, you will want to use some underlayment (plywood) over top of the old floor so that you can maintain the "staggered" or "bricked" layering system. That is one way to maintain the North-South presentation.

Please work with hardwood flooring professionals who have some experience renovating these old gems. They will have seen what worked....and what didn't. Their experience will be invaluable on a project like yours.

I am curious as to why you would not want to preserve the old flooring?

Most old floors can be restored.

This 1906 bungalow began life as an inexpensive 800sf 1BR home. In the ensuing 112 years, it was added on to at least twice. I bought it when it was 1150sf and had been changed in the 30’s to a Tudor style (stucco inside and out, mahogany trim and doors, etc). I gutted it and turned it from a 2/1 to a 3/2 with no change in footprint. The original 800 sf of floors were mismatched with later-added different sized and species floors. A tapestry of species and sizes that wouldn’t work at all. I wanted to keep the N-S orientation, so I laid 3/8” plywood on top of this original and put down my new floors.