JT - please don't be put off by the volume of my posting! I feel guilty that skoda isn't getting the benefit of the range of opinions I know this forum can offer. There is a LOT wrong with every design I've done and it would be good to have other input to correct some of those mistakes! (I'm not touchy about it, honest!!)
skoda - I think one piece of advice that Monty Don repeatedly gives on that show you watched is this: Keep. It. Simple. One theme, chose with the site in mind and followed through, tends to work better than lots of different ideas, which inevitably dissolve into something that looks messier. If you like jungle planting, really GO for that idea whole-heartedly. I've only just realised that it's a thread through everything you've written - I would have guessed earlier had I looked more carefully at the things you've already bought. You have the tetrapanax already - which is just an amazing thing, and you seem to light up with genuine enthusiasm for the wonderful range of leaves and forms that you get with jungle planting! So if that's what you love, really GO for it and ditch the white birches and English cottage garden plants to replace them with rather more exotic-looking things! 
I don't think you need to be all Chelsea Flower Show strict about the botanical 'rules' of it - I see no reason not to have two plants from two different places next to each other in a garden if you happen to like the contrast, but do keep the theme intact. If you go for jungle AND grassland or prairie in separate sections, there is a real risk it will look odd because the style of planting is so utterly different.
Climbers for your trellis - trachylospermum jasminoides, or clematis armandii will give you evergreen leafage, the latter is the more jungly of the two, it really does look exotic and will ramble all over the place. You might get away with an abutilon if it's sheltered from frost and sunny - that would give you a real exotic 'hit'!
Aldi tend to have smallish olive trees (often standards) in late spring! However, I'd say they are more mediterranean plants than jungly ones. That shouldn't stop you if you love them, though!