This is interesting stuff nice post. I haven't looked at a sim for the first spot, but I would be interested to see if the solver also has an over betting range on the flush turn. I vaguely remember on some flush turns the solver using an overbet with some most nut flushes and then some off suit Ax with the nutflush draw. I think I often don't add a 33% turn size to IP range so this may be the reason.
I think my interpretation of the second spot would be just slightly different. I agree the K is a great card for IP range which leads the solver to barrel at high frequency. However, I think the 33% sizing is used because the board is paired on the flop. Maybe as you say in the previous spot the solver wants to bet far more widely than just trips/fullhouses so uses a small size.
I ran a sim with 37Tr (instead of 377r) and looked at the king turn. I gave the solver just the option of betting 33% on the flop (which it did at >98% frequency, so a range cbet)
On the K turn the solver is mainly using the 150% overbet. This puts the OOP player in a gross spot with all Tx and 7x. And gets maximum value with hand like AK which is basically the nuts. Whereas on the 377K board AK doesn't want to overbet as the BB will have plenty of trips to defend with.
Similarly this is just my interpretation, lemme know what you think.
I also seem to remember looking at AA4r and on most turns the solver used the small 33% sizing, I imagine because both ranges have a lot of Ax to defend vs big sizings. However, on the K turn i.e AA4K the solver used almost solely the overbet. (I would suggest this is because IP has AK for the top fullhouse whereas OOP does not)