One game we can play with odd launch dates is assume that "commissioning" refers to commissioning after a refit - which in the case of the Brattain
would be in 2345, with the Tsiolkovsky
around 2363, and so forth. Decommissioning a ship for the duration of a refit used to be standard practice not so long ago, after all. And the unique bridge of the Brattain
might attest to a unique refit in the mid-2340s, as opposed to the more modern refit of the second Saratoga
to the generic "DS9 style bridge" specs, or the older blue-green style spanning the E-B through E-C.
OTOH, stardate 22519.5 may be on a different system than the TNG dates - say, the one used in "Dark Page" for the early 24th century...