The presumption is that the sunroof at one time worked well and now is not. Crud, rust, lack of lube may be factors, but perhaps we should consider some simple mechanicals.
One of my W123's was purchased with a weak sunroof retraction sequence. Last Saturday morning I tore that system apart and may be able to suggest a few things you might check, before doing anything with the motor, etc.
An issue may become clear if one analyzes the opening sequence in a fully functional system:
1. Button is pushed; motor activates, pulling cable into receiver tube in the trunk.
2. Forward end of cable is secured within a slide tube (housed between cabin liner and metal sunroof shell). It is the slide tube that may be the problem here.
3. At its forward end, the slide tube is carried
through a yolk assembly -- a V bracket attached to the forward edge of sunroof metal shell.
4. At its trailing end, the slide tube fits over the cable guide tube leading under the metal roof, down the L/R roof support column, to the motor -- a tube within a tube.
5. At about its midpoint, the slide tube is fitted with a washer-like device welded perpendicular to the long axis.
6. At this midpoint the slide tube is carried
through a horizontal strut. This strut is secured, L and R, to two cam plates.
7. The washer and the strut are joined with a U spring assembly, allowing restricted movement.
8. Cable pulls tube; tube moves washer; washer pushes U spring; U spring pulls horizontal strut; strut activates cam plates; cam plates lower aft end of sunroof metal shell; metal shell follows guide tracks into cavity between cabin and metal roof.
At the beginning of the opening sequence on your car, as the motor and/or your helping hand attempt to pull the sunroof assembly to the rear, stop at one inch. As in your photos, measure opening at L, center, R of sunroof edge. This, to determine improper alignment.
If it fails to open further, close it. Feel through the headliner vinyl for the horizontal strut. Activate again and feel for movement. Close. Activate again and gently attempt to aid by moving the strut to the rear.
There is one other possibility. The pop-up air dam has on each end a guide lever, L and R, pinned near the forward corners. The levers themselves are maybe five inches in length and at the rear are attached to pivot points in the sunroof gutter. Possibly one of these pinned areas may have become undone and the lever is jamming, preventing rearward travel.
Please try the mechanicals without forcing things.
If at the end of all that, you cannot determine the location of the jamming, the next step might be to remove the sunroof headliner. The photos appear to show about 1-1/2” of rearward travel. Look inside up at the forward edge of the headliner. That edge contains a metal strip upon which is mounted some sort of Masonite strip. Into this strip are set six or eight friction clips. these bond the headliner to the sunroof metal shell.
Seated in either forward seat, grasp the forward edge of the headliner about six inches on either side of the centerline, pulling down firmly, BUT with perfect control. The trick is NOT to pull down a distance greater than one inch. The clips will pop, center to the sides in order. Possibly the two on the extreme ends may still be seated. Work to either end and do these individually.
The objective is to gently bend the forward edge of the headliner into a shallow concave “smile”. This shortens the horizontal width and pulls the leading sides of the headliner out of its tracks. A larger smile, more of the headliner will come out. Now gently pull the headliner, still smiling, forward and probably down, over the dash. The normal SOP is roof back 2”, free clips, roof fully back, headliner up and out. I’ve done it up or down, same-same, just be careful.
Once inside, all the mysteries that once were the sunroof assembly should all be made plain.
Good luck.