I followed your rules & only got 4. One problem is that after I scored hits at A3 and B3, I had to waste C3 because I didn't know I'd already sunk your cruiser or whatever your size-2 ship is called. But a fun idea anyway.
The easiest way to beat this is to just guess every square in order, like a1, a2, a3, etc. You only need to erase the number at the end and type the next number, so it goes really quickly.