7 cube

A Cube or BCC?
But either are well below the 33 size of the LUT, so changing the LUT size will basically do nothing, although as you have seen the larger LUT may be worse as there is more interpolation happening.
Or the increased interpolation could smooth things more, so be a bit better.
Either is equally possible.

Steve

I have misunderstood your question. I have not done any profile, but relied on LUT conversion from one gamut to another one. The relevant LUT conversion depends on the LUT generation size.

Doing a colour space to colour space conversion is totally different.
It performs a mathematical conversion, not at all the same as using a profile.
And difference in the results will be down to rounding variations in the LUT generation, and as above could go either way.

So what did you mean by 7 Cube?

Steve

the 343 patches I have used to compare the outcomes

Ah - you would need a lot more patches to get a viable comparison.
But as the approach is not valid, no worries.

Steve