So, I don't read the rules the same way you are. It seems to me that establishing a hold is a grapple check, just a certain specific kind of grapple check, and so these abilities that make you larger for grapple checks make you larger for that purpose as well. In any case, I think it's clear that the authors thought it did so: that there is no benefit anywhere listed that explicitly increases one's size for the purpose of establishing a hold is telling.

Powerful Build (and the similarly-worded "Larger than Small" class feature) are clearly meant to make you count as larger for basically everything combat-maneuver-y (combat maneuvers aren't a defined thing in 3.5 but "subject to a size modifier or special size modifier for an opposed check (such as during grapple checks, bull rush attempts, and trip attempts)" is pretty clearly trying to evoke that sort of stuff, as opposed to stuff like Intimidate checks or whatever that might also work out as side benefits), and grappling is so exemplarily combat maneuver-y that it's even called out specifically in the parenthetical in most of these upgrades.

Basically, there's nothing other than straight up size-alteration that will let you do this, but I think that's because the designers thought they already had that covered (and I would argue they do already have it covered), rather than because they actually wanted small creatures to really never-ever-ever be able to initiate grapples with bigger opponents.

That said, even with this restrictive interpretation of the text, we can still grapple enormous opponents quite handily, if we can provoke them:

The step required to establish a hold only applies when one is seeking to initiate a grapple. That means the size restriction can be ignored in the prominent case of an opponent having already initiated the grapple.

The Tarrasque is built to grapple its opponents: it possesses Improved Grab, Swallow Whole, and a +81 grapple modifier. It shouldn't be terribly difficult to get it to initiate a grapple with your halfling without any effort on your part, but suggestion et. al would certainly be effective should the Tarrasque prove hesitant to bite.

Once the grapple is initiated, your halfling can pin the Tarraque, move it about, damage it, prevent it from leaving the grapple, and all that good stuff without having to worry about size limitations. The size limitations are only a problem against opponents the halfling can't taunt into initiating a grapple.

They are different abilities and they work slightly differently

Your interpretation is correct. A changeling PC has no restrictions on the creature type they can change into, only general body shape and size. Doppelgangers can change their size but are restricted to the humanoid creature type (but appendage arrangement is limitless¹). Whether you think the humanoid restriction makes sense or not, it is clearly there and there is simply no way to otherwise interpret it. Similarly, the size differences are also clearly written and unambiguous.

It is clear that the Changeling PC's ability has slightly different capabilities than the Doppleganger monster. Note that these two abilities don't even have the same name and appear to have no connection to each other at all beyond beyond superficially similar.

The two abilities were written at different times and published considerably far apart for two different types of creatures (PCs and monsters). But that is not at all unusual, in fact it is more unusual for monsters to have exactly the same ability as a PC. Monsters follow many different rules and have many different abilities, some that are kind-of similar to PCs but not really (multiattack versus Extra Attack for example).

It might be worth noting that the PC version is based on the "change appearance" ability of the alter self spell. Whereas Shapechanger is ability that many monsters have and each version of it is slightly different. Though actually the Death Slaad has the exact same variation as the Doppelganger.

No further clarification has been made that I can find, but I also don't think any clarification is needed. There's simply no reason the abilities would be expected to be the same.

^{1 - Or limb-itless you might say.}