The fire stick will work for that. It is always powered on usually and if you stay in the app, you can pick up where you left off. I've used expressvpn and nordvpn on it, but I think some VPN apps need to be sideloaded. The Nvidia shield should work in more or less the same way but with a better experience in terms of loading and navigating.

Nvidia Shield is the best on the market but $$... that is what I use and it does not blink when all is running :)

More work and possibly more expensive option depending on what sort of speeds you want in the end is maybe VPN on a router box, like a PFSense build (which can give you more speed that a VPN setup on a regular router). I went the cheaper route and setup VPN on a cheap router ($30 with DD-WRT installed) that only has the Z7+ connected to it. I did set it up in a way that is less secure than OpenVPN (limited to around 30Mbps on my router) on the router, L2TP mode (limited to around 70Mbps on the router), but a test on http://ipleak.net/ seems to show it's secure enough, atleast secure enough for me. And just to compare, my desktop can do 130Mbps which is a little over 1/4 my whole bandwidth, and like I said depending on the hardware a PFSense build could give even more speed than my desktop as it's a whole computer which is made to be a router. And if you go the router route, I think most routers support L2TP, but not sure you can or should do it on the main router, because as I said this cuts your bandwidth down way down to 20% bandwidth for the whole network.

Edit: Actually, how do you know your ISP is the one blocking? I'm guessing you tried a VPN on a desktop to make sure it worked on a VPN?

I use a vpn on my Formuler z7+ with no issues

i saw one on amazon on sale

are you UK based?

Private Internet Access