Any Android box such as the Nexus Player or NVIDIA Shield will support Tablo Connect.
If you are somewhat tech savvy, your other option is to setup a VPN Server where your Tablo is located, then setup a VPN Client at your remote location. Connect one of your current Roku devices at the remote location to the VPN Client and the Roku will connect to your Tablo. This is how I have been using my Roku 3 Model 4200 for the past 4 years remotely.
It should be noted that a VPN connection will only work if you have a fast upload speed at the home location.
Tablo connect can re-encode the file to a lower bitrate but if using VPN, your upload speed has to be as good as or higher than your recording Quality setting.
Not an issue for many, but some, like my case, I have an ok down (12MB) but stuck with only 1MB upload.
I’ve also used an Amazon Fire TV remotely, works well with no need for a VPN. Aren’t the new Sticks cheap?
As for the VPN Server, I run the PPTP VPN Server on the local D-Link DIR-880L router running DD-WRT firmware, Tablo connects to this router.
As for the VPN Client, I set up the PPTP VPN Client on the remote TP-Link TL-WR841N router running DD-WRT firmware. Roku connects to this router.
@Daniel454 is correct, the upload speed where my Tablo is located is 10 Mbps so I am always streaming at “Full Quality”. If your upload speed is slow, then you’ll have buffering issues cause the VPN connection does have some overhead too.
Just FYI, I’ve used the newish Fire Stick remotely with such success that we dropped all our Rokus at home in favor of Fire Sticks. (This is different from the new Fire dongle/box which doesn’t play well with Tablo.) Been 100% solid in remote situations and all my favorite Roku apps available (YMMV). Currently $5 off at Amazon for Valentine’s Day sale (no, I don’t know what that has to do with V Day).