Steve--The .17 Remington and either the 25 gr. Berger or 30 gr. Starke, Kindler Gold, or maybe the 30 gr. Berger would also be quite appropriate for coyotes, especially. I use the 30 gr. Starke bullet as my coyote load for my .17 Remington. Muzzle velocity is 3,900 fps and it is easy on fur, but hard on the coyote population. The bullets mentioned above are not just good for close range shooting, but work quite well out to 250 yards and with good bullet placement they work beyond the 250 yard mark as well.
I have a Savage 12VLP in .204 Ruger that I use as my primary coyote rifle now. I have not shot a Tac 20, but I don't think the recoil of the Tac 20 is much different than that of the .204 Ruger and I can witness my hits on coyote, prairie dogs, etc. in the scope because the recoil is quite light. The recoil is only slightly more than with the .17 Remington. Keep in mind though, that my 12VLP weighs 10 pounds for just the rifle. Your light carry calling rifle will have more of a tendency to cause you to lose the sight picture with the .204 Ruger or Tac 20, but I would think you might still be able to witness the hits. The Tac 20 certainly has the cream of the crop to choose from when it comes to brass availability.
As for bullets for the .204 caliber rifles that are fur friendly, I happen to think that the 35 gr. FB HP Berger bullet fits that bill quite nicely. Quite a number of .204 Ruger and Tac 20 shooters have been giving rave reviews of their experiences with the 35 gr. FB HP Berger bullets for saving fur and putting coyotes down for the count.
You have a tough choice to make when choosing between the .17 Remington and the .204 calibers that are available to you today. I think your best bet would be to get one of each!!!
I really enjoy shooting both my .17 Remington and my .204 Ruger. The 39 gr. Sierra BlitzKing bullets are excellent for prairie dogs as they have an extremely high BC and they fight the wind extremely well. They are a pleasure to shoot up here in North Dakota where we do have quite a bit of wind when prairie doggin'. I do use the 20 gr. V-Max for prairie dogs and will be using the new 25 gr. V-Max for prairie dogs, now that Hornady began making them available late this past summer. They have a better BC than the 20 gr. V-Max and are better suited to my wind conditions. That will be one of my primary bullets for the new .17 Rem I am building. I am also going to give some of the 30 gr. custom bullets a try in this new .17 Rem.
Anyway, you have an interesting dilemma. Let us know what you choose to do. I'll be looking for your posts on what decision your research has led you to.