I just tested this cheap RTD2556 embedded VGA -> DisplayPort board and unfortunately I wasn't able to convert its eDP output to regular DP/HDMI. There are solder points for eDP signals on the bottom of that board, so I soldered shielded wire pairs to DP->HDMI converter, tried various lane configurations (switching wire pairs and polarity around), but I got no image. I don't know if it is the matter of impoperly configured RTD2556 firmare, signal interference, DP->HDMI converter incompatibility or something else.
But here is Chrontel CH7525a which can be used to convert eDP to HDMI (DVI). http://www.chrontel.com/product/detail/15
The chip itself costs probably only few dollars, because I saw it used inside cheap USB-C to HDMI dongles. The chip I got in my DP-HDMI converter was unmarked. It might just have been a DP++ to HDMI voltage shifter (like CH7530A), not a proper converter. Or just a non-eDP compatible converter.
I believe that some day a cheap VGA to HDMI converter with DOS support can be made, i was hoping that RTD2556 + CH7525A would be the way to go, but cannot confirm it yet. I first need to grab eDP screen and check how that RTD board handles VGA.
By the way, few months ago extremely cheap HDMI to USB 2.0 video grabbing dongles were released and they are very good for the money, although they have visible MJPEG compression artifacts. But I work with Atem Mini Pro video mixer which has MJPEG USB2 output too, and the quality is good, texts and lines are sharp and not distorted by compression artifacts, much better than with any USB MJPEG capture card (actually every capture card I used had garbage quality in MJPEG mode, even relatively expensive ones like USB 3.0 Avermedia Extremecap UVC). So it is not impossible to have good quality with compressed output, it's probably the matter of tuning the device.
BTW2 Atem Mini Pro which I mentioned has 4 independent HDMI scalers, while much more expensive (but older) Atem Television Studio will not work at all if you don't match the resolution and framerate on all inputs. To fix this, you would need to buy additional scalers which can cost several hundred dollars each. Few years ago you couldn't set up a cheap broadcasting studio and now you can, so I believe that using expensive hardware doesn't have to be the only way (even if now it is). Especially in home environment.