The plot thicken's, I have just found more info in the reference material I inherited from Tony Edwards/Peter Labbett.
From Tony Edwards notes - “The over stamp was used between about 1907 and 1914 and signified acceptance by government inspectors. I know it seems laborious, but when a batch of contractor ammunition passed proof and was accepted for service it was run through another die and over stamped with the two broad arrows. The outbreak of WWI seems to have put a stop to that practice.”
More from Tony - .303 blanks headstamped: "K /|\ /|\ V"
Cordite Blanks L Mark V, not blanks converted from Cordite Ball Mark V. If they were converted rounds the headstamp would have been K C V, as Ball Mark V rounds were only made during the period when C for cordite was included in the headstamp.
Your rounds date from the period around 1907/8, as they are undated (and thus pre 1908) but do not have the C code for cordite, which was dropped from headstamps around 1907, although formal approval for this was not given until 1913. During this period there were considerable anomalies in headstamping practice with respect to the Cordite identifier.
Also, during this period (c. 1907 - 1913) all rounds purchased from commercial contractors were overstamped with one or two broad arrows to denote government ownership, as yours is.
Is the colour of your K V blanks a very yellow brass? I ask this because I have weighed a couple of these K V blanks and they were too light for normal .303 spec. When I sectioned an example I found that it was made with a semi-balloon head case, definitely not British spec! Were Kynoch trying to save money on a government contract? Seems unlikely.
All the best
Rich