We just recently moved out of the Centro and back into the home I have been remodelling for the past year or so. We had furniture, appliances, boxes of stuff, and even more odds and ends. Besides that, there is just nowhere to park in the Cento except early in the morning and better yet on Sunday.
You can find movers at Plaza Carrillo there by Abasolo and Av Lázaro Cárdenas. They are there to move you like "right now" or at your convenience. You can find them there by their moving vans parked at the plaza. We needed them Sunday morning at 7am and they were there at that time ready to go.
We had a very large place with appliances like washer, fridge, stove, and large gas barbecue. Two livingrooms full of furniture and three bedrooms and countless boxes packed and ready for them. They cam in and wrapped everything with rolls of plastic wrap for protection. The chests of drawers were emptied into boxes but we could have left everything in them as they wrapped them tight so there could be no tampering or damage or worry about things falling out. Our televisions were wrapped in plastic and carefully handled and they used their dollies to get things out without a problem. I think in less than three hours everything was loaded up, moved across town, and put into the proper places in the new home with all the gas and water lines hooked back in on our appliances.
The cost for this was $2,000mxp. I could not have been more pleased with their service and professionalism. No complaint about the price either.