Now the Latvian Defense Ministry has provided the definitive answer (barring major tectonic shifts), and that answer is: 311.94 meters above sea level.
The ".94" bit is a bit annoying, what with it being so close to a nice round 312 meters, but facts are facts.
And the good news is that Latvia just grew by nearly half a meter. The last survey to tackle the question dated from the Soviet era and delivered the information that Gaiziņš was a mere 311.495 tall, which is far less impressive.
The Defense Ministry and the Latvian Geospatial Information Agency carried out all the technical preparations and legislative changes necessary to establish the new recording as fact.
Unfortunately the highest Baltic 'peak' is still the 318m Suur Munamägi in southern Estonia, but it's good that Gaiziņš is growing and hopes are high that if we keep surveying every few years, we may bring Suur Munamägi down a peg or two.