What happens to the voltage at the Vin capacitor (right after the
rectifier) when you apply load?

Transformer rated to 24V @ 12A  doesn't mean it would holds 24Vac at
10A... this 12A specification mostly says that the transformer wiring
and magnetic flux stands to delivery 12A, not related to power delivered
(you can not trust it always).  Note that 24V @ 12A is around 288
Watts!!!... Are you sure this trafo is that big?

Probably you could find a switching power supply to delivery 24V @ 10A
cheaper than the just the trafo... much less weight at least... :)

What do you mean by; "..and a series 2.5 ohm NTC"  ?

Wagner