@petergoode 

Upgrading the firmware might not really give any difference.

As far as getting a better extender. Since you were fine using a single band I would look at getting a dual band extender and trying high speed mode. What happens is the extender will connect to the router on one band, and then provide Wi-Fi on the other band. It's to help give faster speed compared to the default function.

You can use the RE220, RE305 or the RE450. Where ever you grab it, make sure you are able to return it should it not give the performance you would like. You coudl also simply use the extenders to extend both wireless band on your new router. 

One thing to note is that the extenders work in half duplex so the performance is less compared to be directly connected to the router. With high speed mode it tries to midigate that at the cost of a wireless band you can connect to.

Here is a FAQ about it for reference: https://www.tp-link.com/us/support/faq/2479/

@Tony 

Thanks so much for the response!

I am not ignorant nor am I am expert on WiFi...but if I understand how this works, I might get better speed if I use an extender which relays the 5 GHz signal rather than the 2.5 GHz signal.  So, I need to figure out if the TL-WA850RE can relay the 5 GHz signal...and if not, as you suggest, try out an extender which can pick up the 5 GHz signal from the router and see if it can extend a 5 GHz signal adequately.

@petergoode 

The TL-WA850RE works only for the 2.4GHz. If I was in your situation, I would get a dual band extender and test both functions, normal and high speed and stick with which ever works best.

@Tony 

Thanks again for your answer, very helpful.

One final question, if I may ask...

I have done much further research, and now understand that although the 5GHz band might provide faster speed, the signal to noise ratio is much worse than I might anticipate using the 2.4 GHz band, thus I think the distances and walls in my house would make it unlikely that the 5 GHz band would reach far enough.

As such, would there be any reason to anticipate that a newer or higher end TP-Link WiFi extender would in any way work better than the one I have, thinking about download speeds and distances?  As I noted in my first post, I have been VERY HAPPY with the functionality of my current TP-Link device, and would definitely want to stick with the brand if there would be any advantages to replacing it.  My ISP delivers 200 Mbps to my house, and when using WiFi (Linksys dual band router in basement) and the TP-Link extender, I am getting 26 Mbps in my kitchen.

@petergoode 

You are right about the 5GHz band, you will get faster speeds, but at the cost of distance. So where you originally had the 2.4Ghz, the 5GHz band may not connect so you will probably need to move the extender closer. 

Every environment is different so it really comes down to testing to see what you get. If the 25 Mbps has been perfect for you I would just stick with that then and save the money.

@Tony 

I guess I will go with the old adage that "the worst enemy of good is perfection".

Thanks again so very much for the advice...I did not think it worth spending several hundred dollars on a mesh system, I will remain with the hardware in place!