Skagan -
Got to thinking (a dangerous thing) and realized that the general growth habits of eastern pines is quite different than the best western pitch pines, and that may be making it harder for you.
The best hunting is not for sap on the trunks, but rather at the base of large branches where they meet the trunk or where the branches fork, have had a smaller side branch torn off, lightning or critter damage, etc. The smaller beads may look like a dark split pea to split marble and you can tell if they are solid by cutting them off the tree to revel the clear, amber/red cut side.
The Pinyon, Bristlecone and Lodgepole pines I get my best gum from are old mature trees and all have a very craggy and realatively low growth habit with large knarled branches close to the ground - scaly bark. When a real good tree is found (usually growing on a cliff edge) a pint to quart of high grade gum can be had from it with some careful climbing. Ponderosa pine sap is good too, but the lowest branches on mature trees is usually 40-50 feet off the ground. The pine species with a more straight and tall growth habit, smoother bark and high smaller branches are not as easy to collect from and I don't think produce as much useable pitch. At treeline (9-10,000') where these species get stunted by the harse habitat and deep snow for most of the year is about the only place you can easily try collecting pitch from them out west.
Since many of your eastern pines are more along these tall and sparse lines with no low gnarly branches, you may have to look for specific species. I doubt the Red or White pines would be a good choice. Your best bet may be Jack or Fire pine, and some of the southern pines like Pond, Table Mountain and Spruce pines because they are all more compact and knarly and with low larger branches.
Keep at it, and keep us posted on your progress. If all else fails when/if I ever feel up to going on a collecting trip again, I'll try to remember to check if you still haven't scored yet, and send you some Pinyon pitch to try out. Where I live now I can get into Pinyons year round with little or no snow to deal with in less than an hours drive. Bristlecone is about 4 hours away now, and the Lodgepole about 8-9.
WA