All the advise is good. The rats nest could have added to corrosion of cables and connections. The fact that you were having trouble before the nest tells us that it is probably corrosion, loose cables, frayed cables, etc. (connection problems). So cable/wire, as described by others, has to be taken off and cleaned or replaced....and double checked.....Including the battery cable ends. The grease has no bearing on your immediate trouble, it is so that corrosion will be kept away. I guess in Canada it would be a good idea. I have never needed it. Anti-seize is different than copper conductive grease. They are talking conductive. Forget that until all is fixed because you may have to take it all apart several times before this is solved. Leave it all dry for now. DO NOT USE THE ANTI SEIZE.
Once you have done everything you can for the connections and it still is slow and battery is GOOD, then post again with result facts.
Taking apart a starter is no big deal. It is just a DC electric motor. No mystery. Just don't undo the big screws holding field windings/pole shoe to inside of case. Otherwise they usually have two long bolts holding the ends on. (one end, one nose). Armature out. Standard commutator cleaning/buffing, sector spacer grooves cleaning, wire check, new bushings and brushes, dab of oil on shafts, soak oil wick and back together. Study the internet for starter motor diagrams or see manual for your truck.
WARNING: The terms "copper" "grease" "Antioxidant" "Dielectric" "protective" are very confusing in the marketplace. Many Anti seize compounds use some of these words. Many will actually cause corrosion. Some are not for electrical connections. It is why you now have the wrong grease. Search, read and use if you desire. NO-OX-ID by Sanchem, Inc. would be a good choice. (no metals in this compound). Automotive type ground and 12V connections are best achieved with shinny clean surfaces and tight fastening. The copper filled greases are for very high heat situations and may also add to less contact resistance but will not add to current carrying capacity. Which means the copper serves no purpose for this discussion area.
Falicy of adding metals to increase Conductivity:
Many electrical contact greases have copper, zinc or other metals blended into a grease to increase conductivity. In a study for an aerospace company in 1985 it was concluded that putting metal into grease
does not help conductivity. In many cases it reduces conductivity. The United States Department of the Interior Bureau of Reclamation states in their Facilities instruction Journal Volume 3-3 Electrical Connections for Power Circuits in section 6.3.2 that, "Use of grease with embedded zinc particles will cause a poorer connection due to the lower conductivity of zinc".
Seems to be
Good looking
Stuff. 
