Yes, they have faces only a mother could love. Thanks for your kind words on the image!

The 70-300 is not sharp enough to get good results with a TC. MY recollection of the Sigma 170-500 is that it lacked sharpness at full zoom, and was not a candidate for use with a TC. I used that lens with a 10 and 12 mp crop sensor, and a 12 mp full frame camera - and found the performance ok for a consumer grade lens, but not what I was looking for. Shortly after getting the 170-500 and getting rid of it I got the 600mmF4, confirming what I always suspected. Since then I've lightened my load and gotten a used Sigma Sport 150-600 - which was the lens I felt came closest to the image quality I had gotten used to with the 600mmF4 - and I have used it without a tripod 98% of the time. So not only did I solve the weight and baggage issue, I also opened myself up to taking it hiking, and using it for more active subjects - which is hard to do with a lens that could only really be used on a tripod or other solid support (it weighed 12 lbs). I've found the Tamron G2 to be similar in image quality, and it may have slightly better optical stabilization, and it is 2 lbs lighter. But I don't think the build quality is up to Sigma standards.

This is a sample of a female Blackpoll Warbler uncropped and cropped. I can recommend the Sigma Sport without hesitation. I have now taken over 20,000 pictures with it since 2016, and I couldn't be happier with my choice. As a participant in the Nikon NPS program I had the opportunity to borrow the 200-500 and I rejected it - it lacked the image quality, build quality and weather proofing of the Sigma, and it was not 600mm. Nor did it do very well with a 1.4X TC. Besides, I paid less for my used lens than I would have paid for Nikkor, which was selling for $1300 at the time.

I think you may want to consider renting a modern lens instead of trying to extract extra performance from what you've got. I believe it will be an eye-opening experience. While there are some gimmicks like AI assisted resampling - both in-camera and in post processing, and other "hacks" - the artifacts are not with the investment of time and frustration to get just mediocre results. Those solutions merely increase sharpness by manipulating micro-contrast, and provide interpolation so an image with lower pixel count can look cleaner when enlarged, but upon closer inspection there are undesirable artifacts, and a lack of detail that only a longer, sharper lens (of you have a 36mp or greater camera) and, in some cases, with a 1.4X TC - can deliver.

Here is an example combining two methods. I am using an APS-C crop sensor camera with a Tamron 150-600mm lens which is using a generic Kenko 1.4x TC. The lens is set to 400mm (which becomes 560mm with the TC and 840mm when I take into effect the 1.5x crop factor). And it is stopped down to f8 (which becomes f11 with the TC). Now a generic TC can't compete with a dedicated TC designed for a particular lens, but I have found that if I stop down a bit, it makes a difference.

Image 1 is what I got out of the camera. You can tell it is a bit soft. I am actually too far away from the Egret and there is a bit of camera shake.

Image 2 has been fixed using Topaz's Sharpen AI - Motion Mode, Very Blurry Option. The image did sharpen up.

Image 3 takes image 2 and has used Gigapixel AI to double the size by 2x.

Note: The Egret does not have a processing halo. The sun is low and to the left and a bit behind the Egret. Some of the feathers around the head are seeing the sun while the feathers on my side are actually in shadows. I did not have the option to use my feet and move to a more favorable position with the lake blocking any ideas such as that. Plus, where I was, the Egret wasn't even paying attention to me.

Currently I have a FF camera body, 2 lenses that will reach 300mm and 1 with a 500mm reach. I only print up to 13x19 and don't need billboard size images (yet).

Which would be better?:

1. A x1.4 extender will provide a 420mm reach on the 300mm lens with a 1 stop lose of light.
or
2. Setting the FF to Crop mode will provide 450mm reach on the 300mm lens without light lose, but a lose of pixels.
or
3. Shooting at FF and cropping to the same proportions as in crop mode.

I can test 2 and 3, but I don't want to spend several hundred dollars for a teleconverter.

Thanks

Your best option would be #1, but that is not what I would recommend.
I would recommend going places that can get you closer to your subjects. A quick check on the internet will give you many options if you ask the right questions.
Whenever you go ask the friendly folks here where the closest place to wildlife would be in that location.
IMHO, buy a Canon R5 with a new Canon 100-500 mm lens.
IMHO, or buy a Sony a9 (mint used) and a Sony 200-600 mm zoom lens. Much cheaper option than buying a new Canon R5.

I use a Kenko 1.4 occasionally, and for the price, it's a good deal.

https://smile.amazon.com/Kenko-Teleplus-Teleconverter-Canon-Lenses/dp/B00R11B5CI/ref=sr_1_6?crid=3M60VG7OPQHN0&keywords=1.4+teleconverter&qid=1646396505&sprefix=1.4+teleconverter%2Caps%2C67&sr=8-6

Reviews -
https://www.youtube.com/watch?v=zkrwUURyDPQ
https://www.youtube.com/watch?v=T0g5af_ZWFI
https://www.youtube.com/watch?v=8hATfQ1nWMQ

Kenko Chart -
http://www.kenkoglobal.com/photo/Total_Compatibility_Table_PDF.pdf
https://digital-photography-school.com/the-pros-and-cons-of-using-tele-converters-extenders-on-your-dslr/
https://www.lensrentals.com/blog/2009/01/teleconverters-101/
http://www.dyxum.com/lenses/teleconverters.asp
http://www.lightstalking.com/tele-convertors/