Most common cause for the "hopping" is the preload on the brake controller. Back off on the preload and it should settle down. The proper adjustment should be the trailer wheels not quite locking up when doing 25 mph and using the manual application lever on the controller to full "on". If your preload is too high, the momentum of the moving trailer will over-ride the brakes so that it isn't hopping, but, as you slow down, there isn't enough forward pressure on the shoes and they will "grab", causing that "hopping".
Grease on the drums will cause the same "hopping", but, it will happen at virtually all speeds...the drums grab the shoes through galling and it will affect braking at all speeds, not just the last 10 feet or so...
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)