I'm now getting a good luck at the pictures you posted - for some reason they wouldn't open completely when I first read the post. I was puzzled earlier by your reference to a "center pin" - there is no center pin perse, but rather a sleeve, through which a bolt passes - I get the impression that in your case the sleeve and bolt have "bonded" due to corrosion - this will probably cause the bolt/sleeve to tear out of the window weld, making it a very short lived repair.
Think about this - in an "on-road" situation, lateral movement of the body relative to the suspension will occur primarily in a turn due to weight transfer. The weight shifts off of the inside wheels (the body lifts) and onto the outside wheels (the body settles), and we look for ways to limit this effect, such as anti-roll or anti-sway bars.
In an "off-road" situation, there is less body movement due to weight transfer, but there is a greater need for long suspension travel. As you drive through a trail you want the wheel to follow the terrain rather than limit the motion in any way - one wheel goes over a hole or low spot, you want that wheel to travel downwards as far as possible, staying in contact with the surface and transmitting drive, if the wheel goes over a hump, you want it to travel up, rather than lifting the body, and the remaining wheels causing them to lose contact with the surface - the exact opposite of what's needed "on-road".
Incidentally - I take it you're aware that some some folks disconnect and/or remove the anti-sway bar when off-roading, to prevent it from limiting suspension travel, which by the way, I do NOT recommend on a daily driver, that sees only occasional off-road use - I mention this to further emphasize the perhaps diametrically opposed nature of suspension tuning for "on-road" & "off-road" use.
Rubber suspension bushings are usually bonded to an inner sleeve and if circular will typically also be bonded to an outer shell - in this case the link rod. These sleeves are usually tightly secured so that the suspension deflection comes from the flex in the rubber - traditional polyurethane suspension bushings do not function in this way, they are engineered to have a minimum of flex, and they allow suspension motion by allowing the center pin to rotate as if it were in a bearing - this is why poly bushings must be installed with a special grease.
Will stiff bushings limit flex? That would depend on your interpretation of the term flex - they limit deflection and if the desired suspension motion depends on that deflection, as would be the case for lateral movement in a five link design like the back of a first gen GV, then there will probably be some reduction in suspension travel.