I recall around 2013 that I was following 1.5 HD ReMIX -- before it was announced to be coming to North America. So, naturally, I deviated ways to acquire the game in my homeland and figured I could use my pre-existing knowledge of the game to assist me. My first attempt at doing so was to make a Japanese PSN account (which I did) and then buy it digitally when it was released about 6 months before NA. That, however, I did not do. Why? Simple -- it was not released digitally.
Having experienced that, I would have to say not to have high hopes for PSNow support for KH 1.5 & 2.5 as it doesn't follow their typical grand scheme of handling the game.
Recommendation: Pawn shops are cheap -- I mean dirt cheap. One around where I live sells PS3s and Xboxs on sale for $20-$40 and around $60-$100 off sale. I suggest picking one up from there to satisfy your need to play the game.