Since you are good with your hands and set on doing this yourself I'll give you the following pointers:
Service manual is available free here:
http://www.kallhovde.com/pioneer/sx-1080sm.pdf
1. Do not mess with the discrimintator adjustments. These are the 2 adjustments in the T6 transformer. You need special test equipment to adjust them and you CAN'T do it without this equipment, and you WILL end up wth distorted audio and probably no stereo FM.
2. You CAN carefully adjust the front end for best signal strength. Connect a proper FM dipole antenna. Tune to a known good station on the lower end of the dial, the exact frequency doesn't matter, anything in the 80's or low 90's.
3. Adjust T1, T2 and T3 for the highest signal on the signal strength meter. Use a plastic tool, NOT metal, you can break the ferrite cores.
4. Tune to a known good station on the upper end of the dial.
5. Adjust TC1, TC2 and TC3 for highest signal on the signal meter. Remember what number you got.
6. Go back and forth between the low end and high end and keep adjusting until there is no improvement on both ends.
7. Adjust T5 for highest signal level on any station you want, doesn't matter which end of the dial.
8. If this doesn't improve the reception there is a bad component and a trained tech with rf equipment is going to have to trace the rf signal and see where it is being lost.
Tools:
Aven makes a good alignment tool set. Part# 13.016. these are made of Delrin and are tougher than the crappy tools other companies make.
I got mine from Digikey.
https://www.digikey.com/product-detail/en/aven-tools/13016/243-1016-ND/600970
You should also get a ceramic tip screwdriver:
https://www.digikey.com/products/en...ks-picks-probes-tuning-tools/241?k=aven 13222
I can't remember what exact drives the Pioneer adjustments are but I think the kit and the screwdriver are all you need. Some manufacturers use weird slugs with a wide slot and you have to get special tools or you break the ferrite. I can't find the manufacturer's name for my set.