Some different deterministic theses
Determinism is a fairly broad thesis, and some formulations of it does not "work" with Swartz's regularity theory. Below I have outlined some different deterministic theses.
Minimal Causal Determinism (MCD): All events are caused.
Necessarian Causal Determinism (NCD): "[G]iven a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law."[i]
Predictability Causal Determinism (PCD): Given complete knowledge of the present situation and the laws of physics the future can in principle be calculated with 100% certainty.
The first is what I usually mean when I talk about determinism.
The second is, apparently, what is often meant with determinism when others use it. The second formulation is incompatible with regularity theory as it implies that laws of physics (or nature, or natural law etc.) necessitate the outcome which regularity theory denies.
The last is just an idea I had that might be useful. For instance, it implies that nature is not probabilistic which I think some claim it is. People sometimes mistakenly think that since our theory of some phenomenon is probabilistic, then the phenomenon is probabilistic.
[i] This is what the Stanford Encyclopedia of Philosophy writes as the definition (simple) of determinism. http://plato.stanford.edu/entries/determinism-causal/