I recently was made aware of ISO invariance (yeash, a bit behind the times I suppose). If you take advantage of this, and are using it in your workflow, I would be curious to hear about how and when how and when you use (or choose not to use it).
Nobody else can tell you whether it is better to accept a little bit more read noise or clip highlights. That is not a scientific or technical question; this is a subjective one which must be decided by you, the photographer, but based on technical facts, to understand the trade-offs.
IMO, the ISO-invariant bandwagon is premature in many cases, and most cameras or ISO ranges of specific cameras that are deemed "ISO-invariant" are not really so, unless your compositions are "mid-to-high key", lacking in darker tonal ranges. Almost all digital cameras use increasing analog gain going up all or most of the ISO range, and it's only a matter of how bright you want to make the darker areas of the scenes, which determines if there is a visible noise penalty from using an ISO setting lower than standard for your level of exposure.
Many people assume that ISO-invariance can be determined from graphs of noise or DR vs ISO setting, but the reality is that graphs can only clearly show "negatives", not "positives", for ISO invariance. The graphs at DxOMark and P2P are based on monolithic standard deviations of noise, not the actual spatial character of noise, which has as much or even more influence on the visibility and inconvenience of noise than modest standard deviation differences.
Imagine that you had an empty glass jar and containers of red, green, and blue sand. Imagine that you poured red for a while, then green for a while, then blue for a while, etc. By the time you filled the jar, you would have distinct bands of color which could be seen from quite a distance. If you go as far as you can from the jar, where you can still clearly see the separate colors, and someone else picked up the jar, put a lid on it and shook it vigorously, you would see all the color disappear and the jar would look grey to you. Yet, the standard deviation of the sand did not change, nor did any histogram you may have had of the grains of sand. Both P2P and DxOMark data is given in such a way that it is indistinguishable from and assumed to be the "shook up" version of the sand art, ignoring the "poured" or correlated version, and sensor read noise is actually a little bit like the poured sand.