A few points
1. If the device is dead, or cheap, just cut it off above the board,
the board is rare/delicate the device commodity and replaceable, then
each leg can be got out above board, even the solder sucking process
can do this for you. least board heating
2. after sucking all three, I try to jiggle each lead to check its
free/break any small amount of solder left, hole has to be reasonable
clear
3. with a large iron add solder to get a blob on all three, pull
device out and then suck holes after
4. similar to above but rapid sliding of iron over the pins to get all
melted, then pull device
5. back in the old days there were iron tips around for multi pin
melting, I never found them to be too good
braid never worked that well for me
Dave Caroline