Attached is a RawDigger histogram on a fairly typical image which I ETTR, and one with which I am having difficultly reconstructing highlights in with C1P vs. ACR/LR...
Great, that allows to get a bit more specific, instead of having to talk in generalities.
I know that specific image content will determine the specific shape of the Raw histogram, but there are several additional things to be aware of.
Depending on the Raw format, but usually the case, the Raw histogram shows the situation
before White Balancing. That means that when a Raw converter applies WB, some channels could (relatively to the others) become even more shifted to the right. If the Raw converter doesn't allow to manage that ourselves somehow, we are at the mercy of how the Raw converter deals with that.
RawTherapee for example, allows to compensate for the White point being dominated by a single channel (after White Balancing) by proportionally reducing the other channels. But that does assume relatively little clipping of any channel, for the best results.
In your RawDigger example, as I expected a bit, we can see 3 channels (1 only barely) clipped to the maximum in Raw, and that's even before White Balancing. So that will be a challenge. LR will do a decent job of reconstructing the missing parts, but they are still guesses (some of them are good, but not perfect). Capture One (especially with a 'film' tone curve) will only be confused more. To have at least a fighting chance, a linear curve in this and similar cases is a must if you do not want to lose more of what
is available.
In C1, you will still be faced with the clipped/missing Raw data, which will be handled differently. What I would try in this particular case, is to work with possibly the Levels tool by trying to recreate a proper White Balance, by reducing the relative output levels (at the top of the dialog) of the least clipped channels. The most clipped channel should clip at maximum, the others at a lower level. That may produce funny colors at the clipped maximum, but restore color balance at lower non-clipped levels. You can clip the 'funny' highlight colors to White afterwards with another control, like Curves, the same for all three channels.
It's a bit hard to explain, but I hope you get the drift.
Cheers,
Bart