One idea I find attractive is that the Expanse was a relatively irregularly shaped blob that extended at least one pseudopod between Earth and its main TOS enemies, the Romulans and Klingons. Or at least the Romulans. So when Archer's antics dispersed the Expanse, this made possible (and inevitable) the Romulan War - but until then, the Expanse had protected Earth from attacks by these villain cultures.
That would indeed place the Xindi homeworld in the direction of Beta Quadrant, although the majority of the Expanse might lie above or below the galactic plane, thereby allowing for the familiar empires to exist at that plane (and thus making cartography simpler, the way it seems to be in the later eras).
If the Expanse doesn't extend pseudopods between the major empires, it certainly shouldn't lie between them in its entirety, either - 2,000 ly is way too big for that. So perhaps one has to peek around the nearest corner of the Klingon Empire to reach the former location of the Expanse?
However, I still prefer the idea that the Expanse protected Earth and her vicinity from her enemies, so that its evaporation would leave a power vacuum the newcomer UFP could fill. The Klingon and Romulan empires appear to be older than the UFP, and shouldn't have left power vacuums in their neighborhood in the general case. If it only takes four warp-days to reach Earth from Qo'noS, yet the Klingon Empire supposedly covers dozens if not hundreds of star systems, then the lopsidedness of the Empire must have some sort of an explanation, long before the border defenses of the UFP become that explanation.