Does your tower ring for St George's Day, which, as I'm sure we all know, is on April 23rd (unless you live in Stratford-on-Avon, when it is submerged by Shakespeare's birthday celebrations)? In recent years there has been a big push to have church bells rung for St George's Day. This has had the backing of the Church as a whole: from the very top down. It's most unlikely your Incumbent will disagree with it.
At my tower we ring at 7.30-8.15am, i.e. get up, get ringing, get out and get on with the rest of the day! I see the Central Council is suggesting ringing at 6.00pm, probably to allow those who work to get home and then ring. It doesn't really matter when the ringing occurs during the day, as long as there's ringing.
St Patrick gets some almighty celebrations on his Day, not just in Ireland, either. A report on the BBC News said the celebrations in Birmingham are the 3rd largest in the world (exceeded by those in Dublin and New York apparently). It seems perfectly reasonable to me that we should accord England's Patron Saint celebrations in a style that only England truly knows how!