What’s the Best Transition Between Two Unlevel Floors

Kate asks,

Concerning our linoleum kitchen floor which cracks between the old floor and the addition floor:

The house was built in the 1950’s. The kitchen floor is wood with several layers of linoleum. An eating area was added in 1975 with a concrete pad for a floor. The connecting problem threshold space between the old kitchen and the new addition is 2 yards long and 6″ wide. The linoleum has continually cracked. We have put duct tape across the cracks so we won’t trip.

We pulled up the duct tape and cut out the cracked linoleum to figure out a remedy. There’s rotting wood AND the old wood floor is not exactly level with the new concrete. The wood floor may be ¼ inches lower, give or take, differing a little across the problem threshold space. If we poured in a filler between two LEVEL spaces, it would work.

We bought a hardwood threshold to lay on top of the problem area (see below info). I am reluctant to do this because I would rather have a smooth surface of linoleum.

So, is there a solution other than a ½ inch bump of a wood threshold?