The IRS allows about 50 cents per mile for car/light truck operation, and you can bet you're not gonna come out ahead with their allowance, so a 300 mile round trip is costing you $150 in vehicle operation, maintenance and depreciation. Add the employee's wages and overhead, and you can afford to spend a fair bit on freight.
I'd build a good reusable shipping container from 3/4 plywood, glued and screwed with blocking at the corners. 4 x 4's on the bottom spaced properly for fork and pallet jack access (most LTL's have a pallet jack for shuffling freight around in the trailer). If the parts repeat, you might want to add compartments and some lift out false floors to the box. Make the top such that its got a framework that slips into the top of the box. Hold the top on with a few studs and wingnuts, and then band the box with strapping when its ready to ship. Stencil your company name and address on it in a few places. Avoid the temptation to attach the top with a nail gun or drywall screws as the lid and top rim will be ruined in no time.
But first, get with one of the LTL's that runs from your area to the destination and get yourself a rate based on the weight and value of the parts. I think you'll be surprised at how cheap it is compared to what you're spending now. If Southeastern serves your area they might be a good one to check with. Also Averitt. My B-I-L is in the glass business and he gets a lot of shipments from both of them, all in one piece a very high percentage of the time. Shower enclosures weighing in the neighborhood of what you mentioned cost him about $65 from Jacksonville FL to here. I'd avoid Overnite (now UPS Freight). They weren't that great as Overnite, and UPS's handling practices have probably made them worse. Don't know if Roadway is still around or not, but if so they're another one to avoid. They were so bad for damaging goods and denying responsibility that the largest HVAC distributor in NC (based in Charlotte) forbid them to even come on their property.
A well made, reusable shipping container will pay for itself in no time as compared to cardboard gaylords and such, and your parts will have far less likelihood of damage. The trucking companies like strong things they can stack other things on top of as well, because they get less damage claims. A shop near mine built boxes to ship jet engine components to GE and Pratt using the construction I mentioned above with good results on common carriers.