Any of those 5450's should work fine. Google says there's no problem using a discrete GPU with that Ryzen 3 CPU, so you shouldn't have a problem. Both the DVI ports on those cards should be DVI-I, which does the VGA signal and the DVI-D signal through the connector. So you want a little DVI-to-VGA adapter, and a VGA cable.
That converter you linked to doesn't look great, it's basically one of the cheap converters i describe in section g) of the guide, working roughly the same way the TV-out port of a GPU does. It's not really any different to the converters you have that are giving you trouble, which are in theory the easiest way to connect your PC to a CRT TV, though something seems to be wrong with one of yours.
There's a thread on the j-rok used for this purpose here -
http://forum.arcadecontrols.com/index.php/topic,156915.0.htmlI know it's designed to take the RGB signal from an arcade board, which is RGBS, or RGB+composite sync. VGA is RGBHV, or separate horizontal and vertical sync. Crt_emudriver 2.0 beta 13 and up can be made to output composite sync through the VGA connector, over pin 13. You will have to cut the far end off a VGA cable, and test which wires is which with a multimeter (the cheapest one you can find is ok for this, or just beg/borrow/steal one) and connect up Pins 1, 2, 3 & 6 (R,G,B & ground) and also pin 13 for composite sync, to the j-rok somehow. Google can find the VGA pinout, and remember that all the ground/return lines are the same so it doesn't matter which one you use. As i noted before, this is all a bit more work. I like tinkering, and to my mind the results would be worth it, but if you don't want to do this you'll have to look at another option like one of the plain converters you have (but a working one
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Before you settle on a decision i'd recommend reading through the guide carefully and googling for anything you want to find out, and seeing what you think.