Level a linoleum or vinyl floor for bamboo flooring
I have read your question several times and feel there is no simple solution to the problem. Laying any kind of wood floor over an uneven base floor can be difficult with disappointing results. This is especially true with thinner laminates or veneer type floating floors. Seems can buckle or open and the floor can have a hollow feel. 

It is much easier to fill low spots than lower a high spot. You said in your question that the difference is about 1/2 inch. That is a large difference to bridge. Usually the best way to eliminate a high spot is to raise the level of the rest of the floor to the highest level. Cutting down the joist is not a solution unless you are willing to remove the subfloor. You did not say how large the entire room is or how it transitions into other rooms or doorways. That information would be helpful to know. The fact that you installed cabinets before solving the floor issue complicates the fix. 

The first step is to map the floor by using a long true straight edge and or a laser to visualize the contour of the existing floor. This will tell you what areas need to be raised and by how much. The differences will vary over the span of the room.  Since wood flooring can bridge small gaps, creating a perfectly smooth base is not necessary. The goal would be to create a level plane so the new floor will lay flat.  The fillers or shimming can be done with thin plywood, luan, scrap vinyl, leveling compound or a combination of materials. Baseboards need to be removed and reinstalled after the new flooring is installed. This process can be tedious and time consuming, but if done well, will result in a much better finish product. It really doesn't matter what the subfloor fix looks like as long is it leaves a flat surface. Your new floor will cover all that.