Using Voice Contol on the Stream remote and saying 'Audio and Visual Settings, brings up that page where you can access and change the HDMI resolution to Automatic, 4K, 1080p, 1080i, 720p and 576p, and also alter the 4:3 handling which you mentioned
On my actual TV sets I can alter the aspect ration to from 16:9 to original, 4:3 , vertical zoom and 4 way zoom (the two zoom options allow me to adjust both the zoom ratio and the horizontal/vertical positions of the screen
It sounds to me like your old flatscreen may be the problem if the TV ratio settings don't change on that. Can you factory reset the TV?
Have you got a different TV you can test the Stream box on?
Have you tried factory reseting the Stream box? Settings > System > Reset?
If you can't get to those options then you can try the following
Unplug the USB from the back of the box and then hold the power button on the front of the box while plugging the USB back in. (Keep hold of the power button while doing this) Keep holding the power button in when the Welcome screen appears for 5 seconds and then let go.
A menu will appear. Now tap the power button to select which reset option (hard or soft) you prefer. I would try the soft reset option first, and if that fails try the hard reset.
Then hold the power button again for 5 seconds on the one selected option to reset it.