No deal with XSplit. Use restream.io to stream to multiple locations. you set restream as the streaming service in your OBS/XSplit settings and on the restream website you setup all the outlets where you want to stream at the same time
Are you using OBS? There's a plugin I've been using, works great: https://obsproject.com/forum/resources/countdown-plugin.35/
Make sure to follow the directions, there's another plugin (in the description) that you also need to download.
In my experience you won't have much luck with chromecast (with legal devices anyway) as it's an always on hdcp encryption (not unlike the ps3, but at least there you still had analog as an option, up to 1080p even). Do let me know if you find someway around it.
Funny you mention cheap "Chinese ones". Those might actually be the likeliest candidates to get around that.
Myself, I have an avermedia live gamer portable I bought about 3 years ago for 80-ish bucks if memory serves (still don't know how I got that price, still a bit expensive for what it is https://www.amazon.com/dp/B00B2IZ3B0/ref=cm_sw_r_other_awd_FIDcwbYHVVEDG). Took a lot of driver installing and firmware upgrading to make it happy, but it does what it says it does and works with every console on the market (I used it for some wii and ps3 streaming on my first extra life). Even came with a custom analog cable for the PS3. 720p60fps but only 1080p30fps capture, (really wish they had managed 60fps at 1080p, 60fps is all the rage these days).
You can see the results on some of my old twitch highlights from my first year on my twitch channel (peabodyman). Unfortunately I think I only highlighted wii capture.