Rob,
Your questions are good ones, and the attack under Smith is an uncertain one (the RFRA claim is much stronger). But the point of the "secular exceptions" attack--which Alito accepted several times in the Third Circuit--is not that the exceptions show the government is targeting religion (i.e. is motivated by reasons unrelated to the purposes of the underlying legislation). It's rather that the government is giving weight to other interests, enough weight that it's willing to accept some frustration of its purpose by exempting them, and then is unwilling to give similar weight to religious freedom--a constitutionally protected interest that should receive serious weight. The government may be not targeting religion, but it is devaluing it from the rank of important interests.
I don't think the small-employer exception to the HHS mandate, or a small-business exception in laws generally, is "driven by the underlying purposes" of the law as you suggest. Rather I expect that here, as elsewhere, it's primarily driven by a concern that small businesses experience a disproportionate imposition from the rule. And then the argument kicks in that religious freedom interests should receive similar consideration, because those organizations likewise experience a serious burden, unless there's a compelling interest in making the distinction. Although the government might respond that the reason for the small-employer exception is simply that each one does not undercut coverage as much as each large employer, we all know the obvious logic of aggregation across a category. Here, when you exempt all entities under 50 employees, you cut out 20-40 million employees and (I believe the statistic is) 90-some percent of employers. For the government to accept that big a hole in the mandate but then to say religious organizations deserve very little accommodation may not target religious conscience, but there's a decent argument that it significantly devalues it.
It's true that if this logic applied every time a secular exception were made that compromised the government's interest, then Smith would be effectively overruled. But Alito adopted this logic in the Third Circuit several times--most notably in Fraternal Order of Police v. Newark (1999)--so he might lead others on the Court in that direction. And there are middle positions where a court can say there are enough secular exceptions, with a wide enough range of effect, to indicate that the government is treating religious freedom as significantly less weighty than other valued interests. The HHS mandate not only has the large holes in coverage, but it provides some of them on an individualized basis--the hardship waivers that have been given to many employers--and Smith (in order to preserve Sherbert v. Verner) had identified that as a category where the compelling-interest test still applies.
It's also true that any move in this direction would limit the effect of Smith and get the courts involved in ordering exemptions in some imperfectly-defined category of cases. But we just saw the justices unanimously limit the effect of Smith in Hosanna-Tabor, so they might do so again. The "secular exceptions" approach also, as compared with the straight-up "compelling interest" approach, leaves the government more room to control whether it must grant a religious exemption: it can avoid doing so by refraining from granting other significant exemptions.
With that said, this is all still very uncertain, and the RFRA claim is significantly stronger, although still uncertain too.