Height difference in flooring & Should I cover hardwood with LVT?

[Dan Earl]

I have 3/4" hardwoods in the kitchen and have carpets everywhere else. 

This is my primary home. Hardwoods were neglected/scratched badly and carpets ruined by a tenant. Now I need to figure out what to replace the carpet with and what to do with the hardwoods in the Kitchen to make this home right again. 

The hardwood in kitchen would need to be sanded and refinished and carpets need to be replaced with either carpet or LVT (Can't afford hardwood, and do not want laminate or engineered wood)

One of my concerns is the height difference from the hardwood in the kitchen being 3/4 inch higher. The kitchen's entrance and floor height difference is on a doorway length entrance only (see picture). 

What would you do in this situation?

I have been thinking about covering the hardwood with LVT since it would be the same floor all over the house instead of having lvt next to hardwoods and LVT is easier to clean/maintain. Not having to live through the restoration process of sanding, staining and poly is a plus too, but I am not sure this is the right choice since hardwoods are higher value than LVT. It would be floating LVT not glued. 

Also, there is the height difference of 3/4 inch. Floor guy says he would put a transition piece and it will still look good, but I don't know if this is considered done properly. 

It was suggested that I install luan to increase the height of the floor and try to match it to the hardwood, but that is a lot more work and I am not sure this is even a good idea.

What would you suggest I do to these floors? 

Thank you for reading this and thanks in advance for any insight or suggestions. 

By the way, there is a possibility I may sell this home, but that has not been decided yet. Still need to fix these floors now.