My completely stock 2007 Classic LBZ started throwing the P087 codes under similar towing conditions as yours. Went through the the whole fuel filter head & fuel line replacement. Never did some of the tests you mention though. After research and careful consideration I installed a Kennedy twin lift pump, economy/tow ECM tune, and mega filter install. Purchased one of the fuel pressure gauges from Kennedy as well to verify correct operation. Extremely happy with the outcome and have not experienced any codes since. I know this is much less technical than some of the diagnostic tests you are discussing but it is the extent of what I am comfortable performing myself, and from what I can tell from viewing other posts it seems to resolve the majority of the issues. As you can tell I don’t post much and have relied heavily on the wisdom of some of the very knowledgeable folks who have already responded. Just wanted to share what worked for me.