I don't know why you bother with the HD 709A profile, which appears to be a generic profile intended for use with TV sets. The name implies that it's based on Rec 709, which is an old broadcast standard, with sRGB primaries, D65 white point, but a 2.4 gamma.
All you ever need is a custom display profile that describes your U2413, made with a calibrator. That profile can be built on any of the monitor's presets (as long as it stays on that preset), but it's always best to set the monitor to native/custom. This uses the full gamut of the display without any limitations.
The U2413 more or less covers Adobe RGB. But that's not important as such, it doesn't have to match. The profile describes the monitor as it is, with its native gamut.
The more I get into color and devices, the more i see how utterly and totally screwed up everything is
Don't let red herrings like the HD 709 profile confuse you. Just forget that. You only need to keep your eye on two profiles - the embedded document profile, and the display profile. These two constitute a complete chain.
And equivalent for print - document profile > printer/paper profile.