Am pretty sure the BAT front C/C plates are Specialty Products No. 89675,
http://www.spcalignment.com/componen...tion&pid=89675
BAT doesn't list them in their Contour/Cougar catalog updated June 2016.
I've never been particularly impressed with the engineering in the SP Contour C/C kit, they seem to be weak and subject to bending and distortion, and there is some searchable info here about them potentially causing breakage in the top stem of certain brands of front struts, it might have been Konis.
If the car hasn't been hit, and you don't need them to correct an alignment problem, and you're not looking for extra camber and caster for racing or open tracking, you're probably better off without them, just use the stock upper strut mount components.
Gorman is right, the upper front rubber mounts which support the strut turning bearing and the front spring load have been known to collapse and allow the mount on top of the strut tower to gap away from the sheet metal. The best solution is to replace them with a part of known good quality from a supplier like BAT. Buying these parts from an online supplier like RockAuto is a crap-shoot, some of RA's low cost suppliers don't use rubber of the correct stiffness (durometer), resulting in early failure. I've parts from RA with rubber durometer all over the map in aftermarket lower rear engine roll resistors for the V6 Contour.
For the shifter, go underneath behind the driver's front wheel with a light and look up where the shift cables connect to the levers on the shift tower, the rubber bushings at the ends of the shift cables are often missing or woggled out. This will cause a lot of free-play in the shifter. Shifting notchiness is defined differently by different folks. Difficulty getting into gears can be from bad or missing shift cable bushings, or it can be internal to the trans such as worn synchro assemblies, or even using the wrong lubricant in the transaxle.