A spoilt ballot is a very weak way to send a message.
You make some very good points, but I suppose it also depends on whether your intent is to actually send a message (whether PA or not) or simply to participate in something that you believe is a positive thing to do in the best way that you feel you can.
I think the very fact that tactical voting is accepted as 'A Thing' in the first place is testament to the many failings of our system of 'democracy'.
Also, just as spoiling your ballot could equally indicate a rejection of the choices on offer or a mistake, staying at home instead of going out to vote could also be interpreted in different possible ways: that you don't deem any of the candidates worthy of your vote OR that you are struggling (practically/physically/intellectually) to engage in the voting.
By way of analogy, take the instance of elderly people internet use. I realise that many older people happily do go online regularly, but a great many don't at all. You could have endless schemes designed around helping them to understand it, accessibility for those whose eyesight isn't what it was, ways to help them find, afford and set up the right hardware etc. - but you have no surefire way of knowing how many people are frustrated at not getting the help they need as opposed to those (I'd guess the majority) who simply aren't interested in the slightest and do not want anybody trying to get them online.
I'm not suggesting it would happen anytime soon, nor am I saying that it's more incumbent on women than men because of history; but if you end up with huge majorities of people never going out to vote at all, you leave the door open for those who get into power (voted in by a minority) to claim that democratic elections are clearly not what the people want - that they manifestly don't care or trust themselves to make the right decision and are happy for 'wiser' people to choose the leaders on their behalf. This is exactly one of the 'arguments' that was made repeatedly in favour of continuing to deny women the vote: men were more knowledgeable about politics and thus better-placed to make that choice on their own, especially as the womenfolk had other things such as housework and babies with which to occupy their little minds.
Regardless of how you use it, 'use it or lose it' could eventually end up applying to voting, just as much as to anything else.