I'm afraid you're out of luck on using the oakie bushing puller to remove and oakie bushing. I believe the front bushing is much thinner because of the sleeve that holds it and the rear bushing and seal in place. With the driveshaft in place, there just isn't enough room to get the puller in and grab onto the bushing assembly.

You MIGHT try using the bushing puller, but I expect that even if you can hook on to the front bushing that supports the u-joint yoke, the best you could hope for is to pull that bushing out of the oakie bushing sleeve, leaving the sleeve, rear bushing and seal in place.
I attempted to build a puller for the original bushing out of some exhaust tubing and failed miserably. Wound up ordering a puller from the Filling Station, used it for about 15 minutes and sent it back for credit.
I fear that pulling the differential is in your future.
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HERE is a link to Kevinski's oakie bushing horror story.
