Dex VI is still the recommended fluid for the 6Lxx series transmissions, I wouldn't use a different spec fluid formulated for the specific issues of the 8Lxx series in your 6L45 because it just adds another unknown to the shudder issue and it isn't needed or recommended for your transmission. Also avoid the temptation to use any "magic mouse milk" additives from the auto parts aisle which aren't good for your transmission and create a new and more expensive set of issues.
Try a full tank of 91 or 93 octane and see if that changes the behavior towards the end of that tank run. The 3.6 is a rather high compression engine and direct fuel injection allows it to perform well with 87 octane HOWEVER the transmission programming is optimized for fuel economy under light/moderate throttle and it will be in a higher than optimal gear range under circumstances like where you are experiencing shudder symptoms. This high load/low RPM engine operation leads to detonation of the fuel air charge and the chugging you are experiencing can be symptoms of both the detonation and the engine adjusting timing to reduce detonation. Winter fuel blends are often questionable so trying a different octane preferably from a different station is a simple diagnostic.
A failing coil pack often first shows up under the conditions you note. A flashing CEL along with trouble codes won't be set until there is a sustained heavy misfire, this is to avoid nuisance warnings to the driver but it means that you will NOT get a warning for every misfire episode if it isn't sustained (both in time and consistency of misfiring). A failing plug can also cause this issue, heavy engine load at low RPM creates a compressed mixture that is more difficult to cleanly ignite so problems in the ignition system show up under these conditions. If you have to replace a coil pack, also replace the associated plug because a failing plug can damage a coil pack either by allowing excessive voltage to build up (gap too wide) or excessive peak current (plug leakage).
A code scanner with live view capabilities will show real time counts of misfire by cylinder even when you don't have a CEL. With a failing pack or plug, instead of a full misfire you will get a "poor fire" but the scan will show the counts for this by the time it gets serious enough to create significant shudder. Very precise crankshaft speed sensors measure the periodic brief increase in crankshaft speed for every cylinder firing event and if the expected increases don't occur or are weaker for a couple of cylinders that data will be captured. To best diagnose which cylinder is causing the problem, choose conditions that hold the powertrain in the shudder inducing condition for a period of time such as a slight throttle increase on a grade to hold speed but not sufficient to unlock the converter or force a downshift. Putting your transmission in manual mode will assist in doing this since it won't automatically downshift from the selected gear unless the road speed drops too far regardless of engine load.
Torque converter lockup clutch induced shudder is not common with the 6LXX family unlike the 8LXX family which has a very different "squashed" converter so that it can fit in the same space as the older 6LXX family.
GM currently has multiple auto transmission fluid specs for their various transmissions with the older 6LXX series still using Dex VI which is also the spec for the transverse mounted 9 speed FWD shared with Ford , the 8LXX requiring Dexron HP, and the new 10 speed longitudinal series (shared with and design led by Ford) which require Dexron ULV. When troubleshooting an issue, don't add additional variables like the wrong spec fluid which will have a different modifier pack and operating viscosity compared to the correct spec. For the same reason, avoid the multiple spec labeled "universal" ATF.
Rodger
