I'm really enjoying the experience but my beard is quite tough around my chin and I'm finding it doesn't get quite close enough.
Is my best bet to get a more aggressive razor? Or is it too soon for that and it's more likely that my blade angle is wrong? Or should I start exerting the tiniest bit of pressure in the difficult areas?
Don't get me wrong, three passes and most of my face is very smooth. However there are a few areas that are still rough after three passes and I feel that this shouldn't be the case, as I have to go back over them with a sort of shuffling action (which I read about in a YouTube video!).
I've no idea about the products you've used other than the Palmolive stuff, so sorry if you've already tried what I'm about to write.
I find that I'm a lot more confident during against-the-grain passes if I have popped a shaving oil on first. It just adds that extra layer of lubrication. You can get them cheap, too (around a pound). Also, have you used any of the better shaving creams? I like the Palmolive products, but have found St. James of London, Truefitt & Hill (currently on sale), and above allow me to be bolder with the blade.
This all means that I can apply some pressure, and even go back and forth over troublesome spots. If in doubt, use short strokes.