It could easily be that simple. First, just try just moving the shifter around, with the handle pulled back so it moves freely. The shifter has detents and the tranny valve body has its own detents. The task in adjusting the cable is the get the two to align. I never had much luck using the FSM's "count holes" method. I like to adjust the cable when the pan is off for a fluid change and I can see the detents on the "rooster comb" from below and insure everything aligns.
A small data point. The tranny in our 1996 minivan stopped working in reverse just before a road trip. I had to be real careful not to park where I couldn't roll it back by hand. That is a 3-spd "Torque-flite" tranny (A-413), almost identical inside to a 1966+ 904 (i.e. lever shift w/ internal parking rod). I later tore it down for forensics (after installing a used one) and found the L/R servo had a torn rubber piston seal. I could have replaced that from below. Anyway, I later rebuilt it and found the clutch plates almost worn and their inner teeth worn to triangles which would soon slip.
That said, your tranny is not hard to rebuild, and requires no special tools, just large flat screwdrivers and big snap ring pliers. But do get the rebuild manual since clear step-step w/ many drawings. I bought a rebuild kit for my 64 & 65 904 for $50 on ebay (w/ steels). I recall rockauto has shown it off and on for ~$70. Yours has the multi-wrap band, so insure you turn the adjustment screw per FSM (5.25 turns?), not the ~2.5 turns for later single-wrap bands (unless you install one of those). There are also a few upgrade kits you can get (shift kit, ...). One upgrade is a longer servo piston that can't **** in its bore, which could be your problem.
