I think you have plenty of clearance. Get some shims. They're cheap. The odds of a shop having the correct style shim (any actually) are slim to none at best.
I still recommend you do the alignment yourself. Whoever you take it to has likely never even tried to do one on a vintage car like yours so their skill set is no better than yours. They are used to putting a car on a rack, having a computer tell them everything. Modern car alignment adjustments are simple, straight forward and easy. When they realize they need to pull control arms loose and slip in shims...likely over and over as they try to figure out how it works...I promise you they will get frustrated and at some point say "close enough!". If you do hire it out make sure you get to see the final set-up as it is measured on the car (I tend not to trust people) And make sure your wheels are properly set/centered within the wheel opening.
My alignment now seems perfect, so I am curious: Would I expect to add shims or remove shims with doing this drop?
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