Ours goes into a shallow (2" sides) cardboard form-fitting box that fits perfectly on the floor behind the driver's seat. It has no where to go. We use it a lot and have had no dripping grease: a lot of carbon deposits-yes. That's why the box. A very few black crumbs inevitably rattle down to the cardboard on rough roads. It gets the once over after a few uses, mostly to clean the grill itself.
As far as storing anything on the floor of the TC, I am very covetous of our precious little floor space and only store something there as a last resort. Whatever you store there is always in the way. Always. At least on an 8' 6" Smalllance.
jefe
'01.5 Dodge 2500 4x4, CTD, Qcab, SB, NV5600, 241HD, 4.10's, Dana 70/TruTrac; Dana 80/ TruTrac, Spintec hub conversion, H.D. susp, 315/75R16's on 7.5" and 10" wide steel wheels, Vulcan big line, Warn M15K winch '98 Lance Lite 165s, 8' 6" X-cab, 200w Solar