That should be doable. If there's a limit, then a patch can probably fix it. For example, I tried a USB-C to VGA adapter which wouldn't go higher than 160 MHz. I patched the Skylake driver so it will allow up to 360 MHz (but the adapter tops out at 330 MHz).
There are HDMI to DisplayPort adapters. I think they are limited to 4K @ 30 Hz. I have one that let me do 2560 x 1600 @ 60Hz. I'll see if I can find a display that can do 4K @ 30 Hz. Maybe I'll try the HDMI to DisplayPort adapter with an active DisplayPort to HDMI adapter and try connecting to the big screen TV.
There are HDMI to VGA adapters. The one I got let me do 190 MHz (but I think it's supposed to only allow 165 MHz?). That's not very good compared to the USB-C to VGA adapter I have.
I got HDMI to Dual Link DVI to work with my Apple 30" Cinema Display 2560 x 1600 @ 60 Hz. This used the HDMI to DisplayPort adapter and a DisplayPort to Dual Link DVI adapter.
I'll try those adapters on a Gigabyte Z170N Gaming 5 (which only has a DVI and a HDMI 1.4 port) and let you know how it goes.
SwitchResX has a good GTF, CVT, and CVT-RB calculator that I use to make custom screen resolutions to match the max pixel clocks of the adapters and the max horizontal and vertical refresh rates of the display.
The Intel Graphics control panel in Windows lets you make custom resolutions without restarting the computer. It doesn't show the pixel clock of the resolutions you create, so you should have a GTF, CVT, or CVT-RB calculator handy (maybe another Mac running SwitchResX).
Ubuntu has the xrandr (shows and adds resolutions, and EDID), cvt, and gtf command lines. Ubuntu also lets you look at the DCPD info from the DisplayPort adapters (but I guess you won't see the info for the DisplayPort of the HDMI to DisplayPort adapter).
/sys/kernel/debug/dri/0/
There are online GTF, CVT calculators and EDID viewers (to translate the hex output).