I'm not an expert on axle positioning by any means but I have done it once, both left/right and fore/aft so here are my observations.
If the results from using the alignment tool indicate that the axle is improperly positioned, the lateral positioning of the axle is done with the locating strut that ties the axle laterally to the car body. If the results show that the axle is improperly positioned fore and aft (in other words, more or less than the 280 mm dimension of the alignment tool shown above), then there is method of moving the axle fore and aft while keeping the pinion shaft of the differential horizontal. It is to adjust the "a" dimension shown in figure 8.17 on page 139 of the Haynes Mercedes-Benz 230, 250 & 280 1968 thru 1972 Owner's Workshop Manual, and is also allegedly shown in the Big Blue Book in Figure 35-4/21. My BBB does not show that sketch and dimension (that section is missing from my BBB), but my Haynes manual does show it. The dimension is given in the BBB on page 35-0/1 as, "Check distance "a" between surface of joint flange and support of rear axle suspension (see Fig. 35-4/21) .... "a" = 158 +/- 1 mm . The joint flange is a ruler laid vertically on the pinion shaft flange surface that the driveshaft U-joint bolts to, and the "support of the rear axle suspension" is the front surface of the curved I-beam cross-section carrier that the axle hangs from, which is attached to the rubber mount in the trunk. The measurement is taken from just below the rubber mount where the carrier I-beam is vertical. The axle can be positioned fore and aft on the large pivot bolt around which the left axle and the differential "pivot" during jounce and rebound. The procedure for adjustment is described in the Haynes Manual (but not well) and I assume that section 35-4 of the BBB, if you have it or can find it, also describes the setup of the "a" dimension. Maybe someone in the group has and can provide Figure 35-4/21 and the BBB description of the "a" dimension adjustment.
I managed to get mine changed by trial and error and some careful plastic hammer work. My car's previous owner had moved the axle substantially, but I don't remember which direction it was from where it is supposed to be.
Good luck if you need to move the axle fore or aft, and I really mean that. It was not fun.
Tom Kizer