Has Earth's geological activity calmed down in the past 250 million years?

The large-scale volcanic eruptions you mention are called Large Igneous Provinces (LIPs) and are probably linked to mantle plumes. They have been investigated for quite some time now. Ernst & Buchan (2001) built a database of 300+ LIPs and used it to analyse their temporal distribution, among other things. Here is the age spectrum they obtained:

... ‘well-established’ and ‘probable’ plume head events occur throughout the geological record since at least 3500 Ma, and probably since 3800 Ma, with no plume-free intervals greater than about 200 Myr since 3500 Ma. Plume head arrival does not follow any obvious periodicity...

If you look at the cumulative frequency diagram, there seems to be a increase in event frequency over the last 150 Ma:

There are periods when plume activity appears to be more intense than at other times. These intervals are identified by steeper slopes on a cumulative plot of LIP frequency. The most prominent are at 2800–2700, 2200–1800, 150–0 Ma and more speculatively at 1300–1100 Ma.

But as the authors explain, this is a bias due to the fact that the recent record preserves both oceanic and continental LIPs. However, the oceanic crust is consistently recycled (it's nowhere older than ~200 Ma), thus older events are continental LIPs only. If corrected to include only continental LIPs in the recent (< 150 Ma) record, the trend seems "normal" (dotted line).