It may be better to bring down their total effective power then their flexibility. The entire poitn of this clas is to let you shift into whatever form is convienent at the time, while still allowing you to be flavorful with it. Having a portion of your evolution points fixed drastically reduces the flavor of this class. Instead of being able to shapeshift easily, as I am implying by the title "true shapeshifter", you more likely have a standard chassis that you swap additions to. I'd prefer "I turn into a fish monster and dive into the water" over" I grow webbing on my hands and gills". The latter type of abilties could be an interesting class feature, but the former is what I am going for, and it feels much better as the sole ability of the class.

As you pointed out, what I said implies more of a limit on the delta of your shifts, so you are more likely to shift as little as possible to accomplish what you need, then leave it, which also doesn't fit the concept I am going for.

A rounds/day system allows them full flexibility while they are shifting, and hence fits the concept best at those times, but this character will be especially useless outside of those times, and greatly hampers some of their intended utility. Any application of their shapeshifting that lasts more than a few seconds is no longer feasible, since that takes up a large amount of your abilities for the day, and you'd only have a matter of seconds anyways.

My goal was to have a lower max effectiveness than a summoner/eidolon combo, and make up for it with this flexiblity. I considered double the action economy and a decent spellcaster a pretty hefty tradeoff.

And analysisng the level 20 capabilities of both, the summoner gets to turn into their eidolon, effectively doubling their combave force (more or less). A shapeshifter can shapeshift as an immediate action. I got this idea based on master transmogrogifist(however you spell it) from 3.5, which gained that ability at high levels. Its main utiltiy to allowing you to shapeshift to counter an enemies attack. So if someone throws a fireball at you, you could shift into something fire immune. Its a useful and potent ability, but I don't think it comapres to double eidolon power.