Update: After replacing all the other DH+ devices with Ignition so only the SLC 5/04 with 64K was left, the ENBT/A died and we replaced the SLC 5/04 with a 5/05 to completely eliminate DH+ (and ControlLogix bridge).
On the SLC 5/04, we got tag updates down to 1 s (from ~2.5 s) without overload by adding multiple SVC instructions in addition to setting the flags @pturmel notes. One SVC instruction helped, and adding more between large sections of code helped more.
It's still an obsolete PLC, but less obsolete now. It looks sad next to Beckhoff PLCs and Ignition HMIs breezing along at 10 updates per second, but is comparable to Ignition HMIs using remote tag providers that are artificially limited to updating once per second. Hopefully that remote tag provider update limit becomes configurable at some future point: