no!
im playing it on a built in USB media player on my FHD tv.
Ok, that makes sense. My recommendation stands then- the fastest way to do this is not to do it. Just get a device that can play mkvs as they are and hook it to your tv. Heck, Amazon just put the FireTV on sale!
iv seen those artifacts and low quality signs on a converted video, BUT NEVER WHEN USING WINAVI WITH THE RIGHT ENCODER AND DECODER.
HD-MP4 DOES NOT GET ALL THOSE THINGS YOU MENTIONED
Unless the video is of such a low quality that you can clean things up on re-encode (think silent era films), than ANY re-encoding will ALWAYS give you a final file that is worse than the original.
It is like making a photocopy of a photocopy. It will be worse than the original in some way. Maybe not a way YOU notice, but I promise you Winavi is not a magic bullet. It's final product is worse than the source, maybe you just can't notice it on your equipment.
I mean, from your screenshots alone I personally think you are butchering these files. At the very least you are taking the native audio track and compressing it into AAC, which means that everything you re-encode has a worse quality sound that can't be bitstreamed to 99% of AVRs.
Another issue in the screenshot is that program IS redoing the video stream from what is probably High Profile h264 to High Profile h264. That means, unlike when you re-encode for something like an iPod, you are doing this for NO GOOD REASON. Any decent software would simply take that video stream and drop it into an mp4 container WITHOUT re-encoding. Then you don't need Quicksync.
Look at this video, it will show you how to do this process while keeping maximum quality:
https://www.youtube.com/watch?v=ZNo4Bxh6JGo
Look, I understand that you have something that works and you probably don't want to spend money on something else even if it will work much much better. Normally I help people accommodate these "good enough" solutions because heck I don't want to buy you a FireTV or a Pi. With that said if you post BLANTENT untruths, like this Winavi software is doing everything perfectly and not reducing the quality of your files, I will always call out those untruths.
When I look at that Winavi website and I notice that its price is the same as a box that could just play the mkvs, it makes me wonder if this whole thread is all just astroturfing.
So To answer your ORIGINAL question:
You obviously don't mind a lower quality, in which case quicksync is perfect for you. I don't know if the great and powerful Winavi supports it, but Handbrake does. Here is how to use it in Handbrake:
https://software.intel.com/en-us/articles/harnessing-handbrake
Handbrake is free so that solves your problem.