A Troublesome Dilemma

So, I just found out that the PS4 will not be backwards compatible.
This is quite the troublesome little conundrum I now find myself in.

I had been intending on getting a PS4 fairly soon, specifically due to the announcement of Kingdom Hearts III.

I'm pretty sure I've never mentioned it on this blog before, but I have been a huge Kingdom Hearts fan for many years. I have completed all the current games  (except CoM. Ugh, CoM) multiple times, and can recite the game lore coherently (as coherently as KH lore can be recited, that is) with ease, particularly anything involving Organization XIII.

I remember the first time I played it was when I was 10, in Disney World. I'm pretty sure it was in Innoventions in Epcot. I thought it was a Winnie the Pooh game (it was at the Destiny Islands bit in the first game). I didn't know the name, and could hardly remember the promotional image, but the game itself was stuck in my mind. A few years later, I saw a game called Kingdom Hearts at Walmart, I think. I recognized the main character on the front of the game and got very, very excited. This was the game I had played and loved. We bought it, and began playing it. Needless to say, I was emotionally scarred for quite some time after the whole Heartless ordeal in Destiny Island and stopped playing for quite some time. When I picked it back up again, however, I fell in love.
Fast forward to now. I have fully completed Kingdom Hearts, Kingdom Hearts II, 358/2 Days, Birth by Sleep, Coded, and Dream Drop Distance. I've almost completed Sora's part of Chain of Memories (I'm on the last battle with Larxene, I believe), but I hate the card system, so I don't play it often.

Anyway, the dilemma is...

Do I get a PS3 or a PS4? I had been desperately hoping that PS4 would be backwards compatible. Since it's not, that leaves me with the issue of which one to get.

On one hand, PS4 will allow me to play KH3, which I am very much anticipating.
On the other hand, PS3 has the Kingdom Hearts HD Remix (KHII controls for KH1? Yes please), Journey, and Project Diva f, which are all games I've been wanting.

I'll be sad to miss out on either Kingdom Hearts title. :(

Just my ranting.