This time the benchmark score was 1998 with a message “You can make an extra 100 USD per year with only this computer” – both values being roughly double what they had been before the upgrade.
For the best outcome I set the mining to use both the CPU and the GPU (graphics card). This produced about 3 times as much hashing power as before.
However, given the poor results from last time (about 15p of Monero/XMR mined for 50p in costs) it’s clear that even at 3 times the mining power it would still not be very profitable. This is therefore another dead end.