Here is how to post your Design Dilemma. This photo is almost worst than no photo as far as visual information goes.

https://www.houzz.com/discussions/6417709/unofficial-design-dilemma-boot-camp

yes, I personally would do that on a budget.

Ideally you could feather in the new wood but if that is not something you can do, I wonder if this would be a better transition point?

I agree change the transition site then adding the new floor will work much better.Have you ever refinished flooring , becuse if you have not then please do not attempt to do this DIY

La La made a great suggestion. Cut the flooring back and remove it to the corner and add new transition.

personally, I would wait until I could get enough to have it all the same, all the way through. A floor is expensive, and I would want it to look really good when its finished, and not like I cheated on removing old flooring. If I had to wait a few months, to be able to buy the rest of the flooring, I would definitely do that.

Based on the original picture, I am not sure if the area coming in from the other room is from the kitchen (that the OP wants to keep as hardwod) or is something else.

If it is the kitchen, then LaLa and G&S have given you good suggestions on where to make the transition.

If this is coming in from another room (perhaps just an entryway), I would consider removing the flooring from the other area if it is small, and then you wouldn't have to have a new transition.

If you can get the same width of boards, feathering in the transition would be better than a strong transition.