What you are proposing is a costly fix,though I have had customers pay me to do this, so it may be important enough to you to spend the time/money.
Firstly I would recommend what is called a clamshell reducer. It is a standard transition that handles the problem that you are running into. If that solution isn't good enough, you can make a custom transition that will make a more gradual transition, this is actually one of my specialties that has won me many jobs.
If that isn't sufficient you can install a second layer of flooring over the first (though you must install perpendicularly to the original direction).