So what I did was use a 14 year old PSU and to my surprise, it was able to charge the cap at 25 amps initially with a direct connection from 0 to 2.5 V while the current slowly decreased to 8 amps eventually and poof went the PSU.
(...)
Now the question to ask is why can a 10 year old 350W PSU charge a cap at 25 amps but a new 750 W PSU can't?
Really? But you just said that your 350W PSU
couldn't finish charging the cap
because it blew up. The newer one just gives up instead of damaging itself.
Also, I have serious doubts about your measurement technique, and take the values you report with a grain of salt. For instance, your pencil lead resistor of 2.5 ohms cannot pass more than 5 amps at 12V, and it will also probably catch fire (Pd at T=0 of 60W).
And if you buy a battery charger: Please don't be surprised if it blows up, blows fuses, or refuses to work - they're not meant for charging supercaps either. Your best bet is, as others have said, a rather large CC LED driver that's specced for low voltages - but they're really not very common.
If you're more adventurous, just build a simple buck converter that ramps from 1% PWM to ~20% (assuming 12V in and 2.6V out) over a period of a couple seconds, and cut it off with a comparator when it reaches the target voltage.