Good solder station with nice tip, and a tip cleaner. Make sure polarity of caps is in correctly, do not over heat the pads. Caps can be a little higher in vdc and mfd. , not lower .
Edit : did not see your solder station

Take your time. Remove caps, transistors, diodes exc one at a time and replace. Removes all doubt and headaches. Adding solder to joints makes removal easier. Use 63/37 rosin core solder and preferably 611 or equivalent flux. When removing small IC's - If you come across a stubborn leg that doesn't want to desolder, get off it and let it cool down. I can't tell you how many pads I've pulled as a result of overheating while struggling to remove solder from a single leg. You end up spending way more time having to run jumpers later on then if you would have just took a break for a second or two and let cool before trying again. If you have a desoldering gun, USE IT. Makes a world of difference. Use the proper size tip and remember to heat the joint fully before sucking. Pay attention to your key for proper orientation with IC's when reinstalling. With your bottle cap transistors/regulators make sure you use heat sink compound and a good insulator. You may be able to use the current insulator if undamaged.

Let us know how it goes.

Thanks
Blake

Awesome! Keep rolling on. You will get it working soon enough.

Thanks
Blake