I agree that the McKesh is your best option. We got them for what we hope will ultimately be a Treg cousin - a late model Cayenne S - and have used them on a variety of similar sized rental Nissan Pathfinders as we search for the Cayenne, since noe of our cars are TV capable.
We have a restored vintage cousin 1960
Avion T20 (20'-6" L) & needed the mirrors to see adequately around & behind per CA laws. We go to vintage trailer events around CA a few times a year, so rentals fill in okay for now.
T-regs & Cayennes have some hitch issues you'll want to read up on in the back issues of RV Lifestyles magazine online under their "Hitch Hints" regular feature (it's a Canada magazine). There have been a couple about towing A'streams with the Treg & Cayenne, and there is a hitch reinforcement that is advised - especially with weight distribution.
We elected to go with the Hensley Cub ("Arrow Jr") since our Avion is about 3000# loaded/wet & it's rated up to 6000# - so adequate for the newwer & heavier Bambi's at 4-5000# too, and they are about $1300-1700 vs $2200+ for the larger Arrow for heavier trailers. No WD bars to remove & stow & the jacks are easier than the pry-up chains on other WD hitches at less cost, but the sway is GONE! Only the "stinger" tow bar to remove when parked - or leave it in if locked & not driving off.
As to the 7-pin, the above noted articles didn't mention any issues with reprogramming, but a T-reg online forum might get you better answers.
I can't speak for the brake controller directly, cuz we got a Tekonsha Prodigy RF wireless brake controller mounted on the trailer a-frame with a wireless hand unit that plugs into the DC 12v
power/cig lighter since we knew we'd be renting TVs for a time, but I like that I can have the controller hand unit on my lap or center consol close at hand if I need bump the trailer brakes quickly - rather than reaching to an under-dash unit & possibly compromising steering control &/or vision while reaching/bending forward to bump the brake boost & other controls. More handy with the RF IMHO.
FYI - with 7719# towing capacity on the T-reg, you should also be good for your `78 Argosy!
(Jana's other half & designated hitcher/driver/fixer/etc.)