Are you sure you actually were tightening the brakes?
Did you use the little peep hole in the back of the backing plate?
If so, you can easily back off the brakes instead of tightening them.
Might wish to pull the drums and get a good visual on the condition of the brakes, you can measure the lining to makes sure you have sufficient brake lining. In my state you need the thickness of a nickle to be considered legal any thinner and they must be replaced.
If you are using EZ lube axles or Bearing buddies, you could also have grease buildup that bypassed the inside seal and that grease can get on the brakes and the magnet..
With the drums off, you can now easily adjust the star wheel so the drums just slide on with a slight resistance. Temporarily add the outside wheel bearing and hand tighten it and give the drum a spin. Drum should have a slight resistance, you should here the brakes touching the drum as you turn it, if it stays turning the brakes are not adjusted out correctly. If drum is hard to turn, then you have the brakes set too tight.
Depending on the age of your trailer, you might wish to rework all of the brake wire connections before replacing brake parts. Not unusual for trailer builders to use splices not suitable for outdoor use. The connections get damp, corrode corrosion on the wires in the splices acts like an insulator and now you have weak brakes.
As far as replacing the brakes, yes, generally the most cost effective and easiest way is to replace the entire backing plate. This gives you all new parts including magnets.
Electromagnets generally do not "get weak" with age, they do wear on the contact surface so you do need to inspect the magnets contact surface to make sure the windings have not been exposed.