Hi, good question and knowing the characteristics of flooded batteries and vehicle alternators will provide some insight to help answer the question.
First the guy that sells you the battery will often tell you whatever it takes to sell you yet another device!!
Batteries are self regulating as the voltage (pressure) goes up so does the back pressure,
A one hundred amp alternator will only make close to that briefly when charging a very low battery. As battery voltage rises the amperage declines.
This is a fairly simplistic overview but it serves to explain what is happening at the battery.
Yes there are chemical differences between starting batteries and real deep cycle units, however the intent is to pack as many watt/hours as possible into those deep cyclers. The starting battery just needs topping up as your vehicle is really running just on the alternator
So feel free to use the excess output from your alternator, it greatly exceeds your converter output! AND, motor homes do it all the time without harming either their expensive deep cycle coach batteries or their SLI ( starting, lighting
, ignition) chassis battery.
Real deep cycle batteries need a fair amount of attention to electrolyte levels and terminal cleanliness. Failure to do this is the most common cause of early failure
You don't need a controller and it is only additional expense and complication
Others here have suggested many ways to make the connection, just be sure to have both a switch and a suitable fuse, jobbers sell a fuse with pigtails.
To prevent arcing make sure that that connection is off before disconnecting the trailer harness. G.