We used the SPIRE/FTS instrument aboard the Herschel Space Observatory to obtain the Spectral Line Energy Distributions (SLEDs) of CO from J = 4-3 to J = 13-12 of Arp 193 and NGC 6240, two classical merger/starbursts selected from our molecular line survey of local Luminous Infrared Galaxies (L IR 10 11 L ). The high-J CO SLEDs are then combined with ground-based low-J CO, 13 CO, HCN, HCO + , CS line data and used to probe the thermal and dynamical states of their large molecular gas reservoirs. We find the two CO SLEDs strongly diverging from J = 4-3 onward, with NGC 6240 having a much higher CO line excitation than Arp 193, despite their similar low-J CO SLEDs and L FIR /L CO,1−0 , L HCN /L CO (J = 1-0) ratios (proxies of star formation efficiency and dense gas mass fraction). In Arp 193, one of the three most extreme starbursts in the local universe, the molecular SLEDs indicate a small amount (∼5%-15%) of dense gas (n 10 4 cm −3 ) unlike NGC 6240 where most of the molecular gas (∼60%-70%) is dense (n ∼ (10 4 -10 5 ) cm −3 ). Strong star-formation feedback can drive this disparity in their dense gas mass fractions, and also induce extreme thermal and dynamical states for the molecular gas. In NGC 6240, and to a lesser degree in Arp 193, we find large molecular gas masses whose thermal states cannot be maintained by FUV photons from Photon-Dominated Regions. We argue that this may happen often in metal-rich merger/starbursts, strongly altering the initial conditions of star formation. ALMA can now directly probe these conditions across cosmic epoch, and even probe their deeply dust-enshrouded outcome, the stellar initial mass function averaged over galactic evolution.