I hadn't even heard the term "mini-split" system since a year or so ago, when some in-laws of mine retrofitted a really old farmhouse with them. Really effective for the application they used, although I didn't ask about the price. Something to look into .... !
Lannis
What you call "mini-splits" Lannis are really popular out here. With what can be called at times relatively hot summers and quite cold winters they give the best of both worlds. Not quite sure how true it is but I have been told that the ones built for the NZ-Ozzie market are a bit different in that they throw out a higher heat content than the cold option. The one we have in out open plan kitchen/dining room is 5.8kw on heating and 5.0 on cooling.
If the OP goes that way I would strongly suggest to stay away from any Euro designed models (e.g. Esair, LG, DeLonghi). The Japanese designed ones tend to be all pretty good, but for Hiwalls the Mitsubishi Electric would be my favourite, followed by Daikin.
Bill Hagan did some research on them for his Moto Grappa and got what I would think was a pretty good price for a Mitsubishi Electric model. (Can't quite remember what it was now)