These problem areas are seriously bare wood. Is there any way to repair these problem areas with wax or something? A DIY link with pictures would be the best answer to my question.
If your floors are truly engineered they are 3/8 plywood with a very thin (1/16 ) veneer over the plywood.If this is the case then there is nothing that you can do but replace...sorry, you have worn through the veneer.
A DIY solution for your problem doesn't exist unless you are a flooring professional. In spite of what some people are saying around here, engineered floors can be refinished most of the time. We have done it numerous times with great success. The best advice I can give you is, contact a flooring contractor, let them take a look at your floor and give you an estimate on how much it will cost you to refinish. Most of these estimates are free so you won't have anything to lose. Also, a flooring contractor will be able to give you better advice after seeing the floor than you would get on this forum from people that can't understand the details of your problem. We have some sanding-refinishing advice on our website if you are interested, as well. Good luck with your problem,