I've had multiple cases of tree sap, bubble gum and road tar brought to me when working shows. Being at a show is probably the most difficult time to try and repair cases like these, because you have a ton of people watching, it's usually really hot out, and you have a limited time to work and produce results. This is also the best proving grounds for products and techniques due to the same circumstances. Being a carshow gypsy as well, Junkman's techniques are designed to work and work quickly. I haven't watched your videos yet, but will tonight.
The best results I've had are using a small amount of Adam's All Purpose Cleaner as lubricant/degreaser and a small piece of claybar. I start by soaking the tree sap with the APC (use as little as possible), then reapply for lubricant for the clay. I always break off a real small piece of clay, as I expect to throw it away after use. The clay will lift the impurities off the paint without marring. Make sure to check and fold your clay more often than you would during the standard clay process.
Also, remember to rinse the APC off as soon as the paint has been corrected. I use Adam's Waterless Wash as a substitute for water if I'm at a show.
Always follow up your paint correction with a good coat of wax to protect from future issues.