I am sorry to tell you that you are mistaken about the frame loads.
The "spine" as you call it, or backbone (top tube) is only one path for the transfer of loads.
You are correct that a properly designed frame does NOT require an under engine cradle.
Because the frame gets the required triangulation from other tubes and/or the engine mounting.
The EX uses the engine as part of the frame and the engine castings are designed to carry the loads.
As you understand as you said it is a stressed engine.
The KLR frame does NOT use the engine as part of the frame so it needs a different design.
Your modification to the frame is definitely NOT as strong as it was before because of the way you added the new cradle tubes. However, IF you make good solid engine mounts to use the EX engine as part of the frame by tying the steering tube through the engine to the swingarm mounts you will recover a lot of the lost strength. Maybe enough even... If your engine mount points are well engineered to carry the frame loading and are extremely precise bolt line-up. No oversized holes allowed!
In frame design, think of triangulation, or even better, pyramids, 3 sided pyramids with each corner and the top as the fixed points. It can't be bent, twisted, or distorted without huge forces. A typical motorcycle frame with a double cradle is actually a poor compromise because of packaging an engine. A much better design is the perimeter frame where the load path from the stem to the swingarm can be almost in-line and then another tube (each side) can either be above or below the engine and going from the stem to another tube to create a triangle. Does that make sense? It is late and my brain is tired. Then the two frame side triangles are cross connected and braced.
Your frame mods have broken the load path that went down the front tube and then split into a double cradle under the engine forming a triangle. It would have been MUCH better if you had connected your new cradle at the front tube in one place forming a bent triangle under the engine similar to the stock frame. By putting a cross tube horizontal and then connecting your cradle tubes to it you have turned the cradle into a bent rectangle which has very little resistance to twist. Picture an open cardboard box and how easy it is to deform it by pushing in on any corner.
A motorcycle frame is designed to handle a lot of twist not just supporting the weight of the engine and tying the stem to the swingarm.
I strongly encourage you to rethink and rebuild your frame modification.
It can be done correctly without major expense or time.
First, cut out the tubes you added and then have the correct size TUBING (not pipe) bent to shape that will meet together on the front down tube at whatever height you need for engine clearance (oil filter, etc.). It would also be very good to get short (2"-3") tube that is a tight fit inside the frame tubes to act as internal sleeve stiffeners for the weld joint. Drill a hole through the frame tubes and puddle weld the sleeves in place before welding the new tubes to the existing frame tubes.
Others have successfully modified the KLR frame so learn from them.