I note Barraud & Lund had three items described in the 1851 Great Exhibition catalogue ...You say 'circa 1855' - what is the earliest documented references you have found in English and Swiss literature?
Marine Chronometer, with a model of a newly-invented compensation balance, constructed for exact adjustment to all temperatures.
Marine chronometer of ordinary construction
Very small gold pocket chronometer, a specimen of minute English manufacture.
No mention of half chronometer, but I suspect that it was the 'newly-invented compensation balance' which seeded the term half-chronometer. However in the context of a marine chronometer it's possibly referring to Lund's correcting weight.