Hmmmm, there's a lot to unpack in the details you've provided.
The spec sheet you provided says the monitor has a horizontal scan frequency of 31-38kHz. This means it takes a VGA signal (640x480 resolution) through the HD15 plug commonly called a VGA plug. A VGA signal is 31kHz. This is the lowest resolution your PC or laptop will output by default. You can go lower than this using an S-video port of some type (bad idea) or special drivers depending on hardware.
CRT’s scan left to right, one line after the next down the screen. They don’t care so much about the number of pixels in each line (horizontal resolution). They do, however, care very strongly about the number of lines (vertical resolution) they can display per second. This is the horizontal scan rate. So…
525 lines x 60 fps = 31kHz.
(525 is 480 visible lines plus a blanking interval of 45 lines).
The V-sync knob on the set is V-hold, and is to stop the picture rolling. On newer monitors that function is normally automatic. If you want to up the framerate, you do so by modifying the signal going *to* the set, not with an adjustment *on* the set. And even if you do change the framerate on your PC, you’re going to run into trouble fairly quickly if you try to increase vertical frequency (fps) at that resolution as you’ll hit 38kHz at about 72 fps. And higher resolutions are going to have trouble right away, as 800x600 will only fit at ~56fps, so you’ll have to make a custom resolution somehow. The horizontal scan rate is usually the limiting factor, the other numbers you can normally play with a bit.
TBH at 60p (60Hz/fps) you shouldn’t be seeing flicker. That tends to be more of a problem with interlaced resolutions. Though with the cited specs I'd guess this monitor was intended for early PC presentation use in the mid to late 80's, so maybe it flickers. You might even find that a 400@70p resolution or something from old DOS versions like that looks a lot cleaner vertically, i've seen similar effects from older presentation monitors designed for PAL 576i - they take 480i NTSC but don't look nearly as nice even using RGB. Remember that 15kHz and even 31kHz games look best at native vertical resolution, for example putting a 240p game on a 256 line video mode can make it look pretty bad. You don't want to mess with the vertical resolution if you can possibly avoid it. For video content, going below 480 lines really starts losing detail.
Next, I have no knowledge of the CDO, but I imagine it’s like the megadrive in that it only outputs 15kHz video. Probably 240p, but possibly 480i at a pinch. Most older consoles up to the PS1 only output 15kHz video. This is going to be a problem if the set only syncs to minimum 31kHz (480p, as above) as listed. You will need something like a linedoubler, but to begin with i have no idea what video connection you’re planning to use.
I'll admit i'm not 100% on what you're saying you've got working. If you have more info about what you’ve already done regarding testing, and what you plan to do, we might be able to help further. If the specs you provided are correct, it really looks like this set was designed to take from 640x480p up to only 640x576p, nothing else. And even then that last resolution is over the bandwidth limit...