Not sure if you'll see a whole lot of advantage in switching the 970/1060 around - perhaps a bit, but probably moving up a bit in GPU power would be the best solution.
To that end, wait to see what the fallout is after Monday at Gamescon when nVidia is going to release more information about the upcoming 20xx series of new graphics cards. They may be opening up pre orders next week for the next gen cards, and that will very, very likely have an effect on the currently available 10xx series of cards (ie price dropping). You probably will be able to snag a 1070 or 1080 card for much less in the next couple weeks than what they are currently priced at, as dealers, nvidia, and nVidia's partners/resellers like Asus/eVGA, MSI/etc will want to move out the current stock, and fast.
IMO you will have picked a great time to look up upgrading if that's the route you pick due to this timing, and there will be lots of posts I imagine here and elsewhere about this topic.
For my primary home theater system I have a 1080ti, but ran a 1080 for quite a while, pushing a 65" LG NanoCell 4k screen (we have a home theater room with a projector but I don't use a PC to run that, yet). Both worked fine, and I also run a 970 to a 50" 1080p Sony TV, and it worked really well too for TV/HTPC type stuff, but didn't perform all that hot with games on that TV, the few I tried at least.
IMO your 40" TV (I'm assuming by HD you mean 1080p), a 1080 will no doubt work great, but I think a 1070 should as well. Are you gaming on the TV or just using it for home theater PC type stuff? I'm surprised actually that a 1060 isn't good enough for just TV type applications for a 40" 1080p, unless of course you're playing games on it too, which then I could understand some games not performing as well.