If it were me I would replace the frame. The cost of those materials is not that much compared with the cost of the decking and railing. Then you can fix the span problem, you have a chance to change up the shape/feel and layout if needed and you don't have to worry about it structurally. Especially since you are planning to be there for another 15 years.

Riles

I think you mean the layout is on 24" centers, not the joist span.

It makes no sense to put 5/4 ipe on a 25 year old frame.

Furring the joist with 1/2" strips of any flavor of wood is a mistake.

At 25 years old that cedar deck is at the end of it's life, time for new deck imo.

Yes, the layout of the joists is 24" centers.

Time for a new deck means the whole structure or just the decking?

Yes, time for a whole new deck, imo.

What sense does it make to put high $ decking like 5/4 ipe on a frame that is 25 years old?

I'm with the others. Re-frame. If it's that old it's probably got some other code issues (4x4 posts instead of 6x6, end nailed instead of joist hangers, post anchors vs. embedded in concrete, etc.) and it would be good to bring it up to current code and make it more solid at the same time. You need 16" centers for your IPE anyway.

Post some photos and we can give you a read on any other issues you'll want to fix while you're at it. :-)