Replacing Capacitor - Soldering difficult joint near the electrical path

This is first time experience replacing faulty capacitors from desktop computer motherboard. On Youtube everything seems all easy but in reality not always. Most videos usually show easy placement of the capacitors on the motherboard where they are large empty spaces between the capacitors and the electrical paths.

In this fixes i've try to replace capacitors near the graphic card PCI express expansion slot. The real challenge is the there are quite a number of electrical line path that run closely to the capacitors' leg. During de-soldering and soldering process, I could not avoid to heat at least some of them because too close to the capacitors. Another problem there is no solder iron tips as small as that to solder this thing

This pictures shows how close the capacitors leg and the electrical path. I think i've burnt at least 2 of the electrical line and that's definitely the end to this motherboard. If anyone knows how to solder this kind of difficult joint would you be so kind to share how to do it the right way without heating up or burning the electrical path near to the capacitors.

The other joint in this picture was soldered correctly without damaging the electrical path because there are some empty space to separate the electrical line and the capacitors.