First the speedometer. The cause is most likely a bad cable, but it could just be that the cable has come loose from the speedometer head. Either way you need to take a look under the dash and find the rear of the instrument and see if the cable is connected. If it is you need to unhook it and then either drive the car a bit or jack up the rear and place on jack stands so that you can run the engine and turn the rear axles, what you're looking for is if the inner cable of the speedometer cable turns. If not then unhook the cable from the transmission and remove it and either get a new cable or take the old one to a speedometer repair shop and they can make up a new inner piece if the outer housing is ok.
As far as the king pin bushing goes, those are not something your mechanic wants to take on as there are two bushings and they both have to be reamed to size with a special tool to maintain alignment. Your best option is to get the rebuilt kingpin set. Moss doesn't show that in their catalog, they have all the bushings and the special tool, but don't offer the rebuilt parts as a complete assembly. Both Spridgetmania and Victoria British offer rebuilt assemblies with new bushings already installed and reamed to the proper size. You may wind up needing new lower trunion bushings as well and those are part of the lower A arm. New A arms are available if needed.
'73 Midget (V6)
'59 MGA (I6) under construction
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