Well, what's the situation? Are you coming to see a potential partner? Are you simply coming to see friends and travel? Where will you be staying? What kind of work do you do that you can stay for 6 months and still have an income? These are the kind of things Immigration will be looking at. Also bear in mind the dollar to pound conversion. Your $3,500 is only worth about £1,900 and your $2,200 about £1,100 - £1,200. That's not bad, but if you're staying in hotels and eating out a lot that money will go quick. If you're staying with someone and eating at home more than that will help, but then there's also the cost of travelling while you're in the country and when you go to Ireland and France and entry fees to any places you might be going to.
I don't think you're being too optimistic, but trying to give you some different ways of looking at the situation.