Question about HDMI output on VHS/DVD combo players

I just got a 32" 1080p TV (upgraded form my old 22" Sylvania 1080i dinosaur), and it lacks the composite and S-video inputs; only having HDMI and Component. My Sony VCR/DVD combo player I got from someone throwing it out only has composite for the VHS feed, which the new TV lacks. Yes, I also have HDMI converters (both for Composite/S-Video and Component sources). But when I fed the composite from my Sony combo player to my CVBS-S-Video - HDMI box, no picture came up but displayed normally from composite to my old 22" Sylvania 1080i dinosaur.

Also, the Sony player just died (hey, it was free), so ether way I would need a new one, preferably with HDMI out for BOTH the DVD and VHS signals. So far, I have been looking at these:

http/www.amazon.com/Samsung-DVD-V9700-Tunerless-Upconverting-Player/dp/B000N7VQDK/ref=sr_1_1?s=electronics&ie=UTF8&qid=1448245220&sr=1-1&keywords=hdmi+vhs+player

http/www.amazon.com/Samsung-DVD-V9800-Tunerless-Upconverting-Player/dp/B0014GVYCC/ref=sr_1_3?s=electronics&ie=UTF8&qid=1448245220&sr=1-3&keywords=hdmi+vhs+player

http/www.amazon.com/Funai-ZV427FX4-Combination-VCR-Recorder/dp/B00CCILYDA/ref=sr_1_9?s=electronics&ie=UTF8&qid=1448245220&sr=1-9&keywords=hdmi+vhs+player

And they really don't say (even from customer reviews) if the VHS mode outputs through HDMI or component. What also doesn't help is that some sellers and reviewers say only the DVD output is sent through HDMI. Does any one know if (or have owned) the three in the links send the VHS signals through HDMI? Any help would be greatly appreciated!