We investigate the molecular gas content of ∼ 6 quasar host galaxies using the Institut de Radioastronomie Millimétrique Northern Extended Millimeter Array. We targeted the 3 mm dust continuum, and the line emission from CO(6-5), CO(7-6), and [C-I]21 in ten infrared-luminous quasars that have been previously studied in their 1 mm dust continuum and [C-II] line emission. We detected CO(7-6) at various degrees of significance in all the targeted sources, thus doubling the number of such detections in ∼ 6 quasars. The 3 mm to 1 mm flux density ratios are consistent with a modified black body spectrum with a dust temperature Tdust-47 K and an optical depth ν=0.2 at the [C-II] frequency. Our study provides us with four independent ways to estimate the molecular gas mass, MH2, in the targeted quasars. This allows us to set constraints on various parameters used in the derivation of molecular gas mass estimates, such as the mass per luminosity ratios αCO and α[CII], the gas-to-dust mass ratio δg/d, and the carbon abundance [C]/H2. Leveraging either on the dust, CO, [C-I], or [C-II] emission yields mass estimates of the entire sample in the range MH2-1010-1011 M. We compared the observed luminosities of dust, [C-II], [C-I], and CO(7-6) with predictions from photo-dissociation and X-ray dominated regions. We find that the former provide better model fits to our data, assuming that the bulk of the emission arises from dense (nH>104 cm3) clouds with a column density NH-1023 cm2, exposed to a radiation field with an intensity of G0-103 (in Habing units). Our analysis reiterates the presence of massive reservoirs of molecular gas fueling star formation and nuclear accretion in ∼ 6 quasar host galaxies. It also highlights the power of combined 3 mm and 1 mm observations for quantitative studies of the dense gas content in massive galaxies at cosmic dawn.