I would put it on after.... Leave it out so it comes to room temp and then crumble it over the hot pizza as soon as it comes out of hte oven - the heat should heat it through nicely

I will also depend on the TYPE of Feta you bought - some are very mild and have not much taste really - like the Danish feat- it is very smooth creamy and nowhere near as crumbly, but lots of people like it because it is usually the cheapest and it is very very mild in flavour. You want a good sharp Greek feta in some nice brine...
Reckon your on to something there Lime as i asked DP what feta he purchased and he look dumb struck when he asked me what is brine, LOL
......... Might do as you mentioned or maybe pop the feta on the last 5mins in the oven