There's no such thing as "full LTL"....LTL actually stands for "less that truckload"....
....but most people haven't spent 25 years in logistics so that's ok.
Do you need a liftgate on each end or are they being loaded someplace that's dock high?
You may not need them palletized if you're using the whole trailer, again, depends how they're being loaded (forklift?). There are all kinds of carriers that do this, but don't expect any assistance loading or unloading. You may have better luck with a smaller mom and pop outfit than the big boys, they probably won't want to bother with it.
R&L has liftgate tractor trailers -
There are search engines you can use, plug in your p/u and delivery locations and carriers bid on the trips (not talking uShip). One such is Sylectus.
Second day on Pinside and you're moving a tractor trailer of games?