No reverse

Which engine and transmission do you have? If it's the four speed overdrive, there will be a circle around the "D" on the shift indicator. If you have the three speed, put it in manual low and see if it stays there when you drive forward. If it shifts to second gear, the low / reverse band is broken. That doesn't require a total rebuild but the transmission has to come apart.

To get them out, you'll really want the car on a hoist. It can be done on the ground but you'll need a floor jack, and ideally a helper.

You didn't have to remove the struts or spindles. Doing so means it will have to be aligned when you're done. All you have to do to get the half shafts out is separate the lower ball joints and pry the control arms down, then pull the bottoms of the struts outward. That leaves the alignment adjustments alone.

This is not a transmission you want to rebuild yourself. Cleanliness is extremely important and the final drive gear nut torque is critical to prevent gear noise. If the forward gears are working, the clutch packs and seals are okay. It's more likely there is an electrical problem, a problem with the Transmission Computer, or something with the solenoid pack. It should really be diagnosed before you jump in with the most complicated repair procedure.