Looks like all the suspension gurus are otherwise occupied so here are my comments.
Hopefully you have access to a digital caliper or something equivalent. Have you checked and compared the thickness of the dropped spindles (through the king pin area) comparing left and right sides. Same with the link pin carrier (inside from lower to upper king pin bore). Assuming the link pin bushings are in good shape on the link pin carrier in question and when you mount the link pins in the bushings, are the pins the same distance apart when measured on both sides of the left carrier. In other words, is the carrier bent which could account for the sloppiness?
If the spindles are the same, the link pin carrier is not bent but the distance between the upper and lower king pin bores is greater on the left side, the carrier has probably been hammered out over time perhaps due to poor lubrication or broken or missing fiber washers etc. Could be other reasons too. You just may have to buy a new carrier but I would ask for a measurement of a new one to compare it to yours just to make sure you are solving the problem. Any reputable vendor should be prepared to do that for you.
I'll try and find some specs on the link pin carrier dimensions.
Now measure the thickness of your thrust washer. Our good friends at CIP1 show a thrust washer on their site but with no thickness shown. Call or email their tech support and ask if they would mind measuring the thickness of one for you. Originally you could buy different thicknesses of thrust washers (3.5-4.3mm or so). Perhaps someone on this site might have some of different thicknesses. I looked in all my usual places and couldn't find any. Maybe the CIP1 washer will be thicker and solve your problem. You'll have to let us know the thickness of your thrust washer.
With respect to the link pin shims, here is a photo (courtesy of the Samba) showing how to properly place the shims.
Once this is all resolved, you will need to check the toe in as per the manual. Are you lowered front and rear or just in the front. If just in the front you may need some caster shims on the lower front beam as well. A professional 4 wheel alignment may be in order if you don't know the vehicle history!
My thoughts. If I have missed anything I'm sure we will hear.