Alternatives to aluminum capacitors
Not necessarily cheap, but they have the form factor you need:

Cornell-Dubilier electrolytics

They have different ranges for 5 and 10 year life.

Thickness of the MLP series is 0.5" (about 12.5mm) max.

I would note that these devices are widely used in high reliablity applications and have been around for many years and are expected to be around for many more.

Although some products can quickly become obsolete (a reason for the off-topic rule), this product line is not one of them.