I thought of another angle to get a discounted freight shipment.....surely you know somebody at the local airport(s) in MX who ships and receives parts/equipment semi-regularly through a freight carrier. Explain your needs and ask for a favor. Pay them up front for your shipment and give 'em a big thank you.
If not an option the typical front office of a freight carrier is full of ugly women who want to feel sexy. Walk in like you own the place, give her a big flirtatious smile, explain what you have to ship and politely ask for her best quote. The LTL freight industry is sucking wind just like aviation and they need revenue. Since your bike is basically traveling the I-75 shipping 'lane' carriers which run this route are a dime a dozen.
R&L Carriers, Estes, USF Holland are just a few that specialize in this lane. All R&L trailers have free liftgates too. USF Holland was founded in MI so maybe they have great rates out of that state.....just my .02.