The converter boxes don't have to be great - down conversion is a bit more attainable. This $9 one from Amazon works well for me. You might even try setting the PS TV to output 480p so all the converter is doing is going from progressive to interlaced and see if you like that more. YMMV
Generic Mini HD Video Converter Box HDMI to AV/CVBS L/R Video Adapter HDMI2AV Support NTSC and PAL Output https://www.amazon.com/dp/B00P12BOO8/ref=cm_sw_r_awd_P9EOvbMV725Z4
Edit: Right, need a link there.
I have personal first hand experience with this unit. I was using it with an Android TV stick and it worked just fine. I could dig it out and try with the Chromecast but I'm sure it would work with that too.
*edit Never mind, misread your post. You're looking for VGA conversion. Sorry.
Reviews aren't stellar but after reading through them it seems like the main problem is people not knowing the difference between PAL and NTSC.
Plus, I didn't care about video, just audio, and several reviews said they had no problem getting audio.
I am happy with it, except that it requires power via a mini USB plug. IDK if the VGA adapters require power.
Hope that helps!
One of these will allow that: Generic Mini HD Video Converter Box HDMI to AV/CVBS L/R Video Adapter HDMI2AV Support NTSC and PAL Output https://www.amazon.com/dp/B00P12BOO8/ref=cm_sw_r_awd_b5tsvb0DH9K9D
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