Your salesman is full of deer raisins. It is hard to pronounce any slug round as THE round for a slug gun until it has been tried. There are two things working against the average slug shotgun. First, the barrel is usually not permanently affixed to the receiver. You can improve accuracy on a dedicated slug gun by getting that joint welded, but I do not think it is worth it. If I was going for that kind of accuracy, I would be starting with a bolt-action slug gun. The other problem is the variability from one shotgun to the next and one round to the next. To me, the best way to handle slugs is a 3-point plan:
1) Start cheap and work up. Be aware that the cost to sight in at a given distance goes up dramatically with yardage. Also remember that you do not have a 200 yard deer rifle there. It will do 50 yards fine. You are ahead of the game. Most slug guns require a little bit of work to do 100 yards You'll want to be careful to pick slugs that are meant for a rifled barrel. Some are. Some are not.
A lot of guys use sabots nowadays. To me, the most endearing aspect of shotgun slugs is their mass. I once heard a 45 year-old woman tell a 20 year old woman "Dear, you just haven't lived until you've worn real silk stockings!" My feeling is about the same for the all-lead foster slug. Remember that sabots are a two-edged affair. What you gain in potential distance you give up in mass. A slug at close range on a deer can be a moving experience. Trust me: mass has its advantages.
Also be aware that sabot performance are more hit and miss than a standard slug. There is a lot of variability. You may find one that performs well or you may find that $200 into the search, you still do not have a good sabot load for your barrel.
You've already discovered another secret: 2 3/4" slugs in a 3" barrel. You don't HAVE to shoot 3" slugs.
2) Pick a range and a budget. Be realistic. 80% of my deer have all been taken inside 80 yards. The vast majority have come inside 50 yards. That's with all methods with a heavy bias towards rifles. Guys dream of deer at 200 yards, but most deer get shot remarkably close. If you are already grouping at 100 yards, you are ahead of the game.
When I first got started with slugs, I took a $2 box of Remmie sluggers out with my Rem 1100 smooth-bored deer barrel and shot a cloverleaf on a pie plate offhand at 50 yards. I never worried about it after that. When I got my Mossberg 500 with the rifled barrel, I tried three different slugs and settled on 2 3/4" Brennekes. Those were going in the same hole at 50 yards offhand. I did not push it beyond that.
Why 50 yards? I got into deer hunting as an archer, so I always thought in terms of archery distances. All my stands were set up as archery stands and shotgun season was sort of a conciliation prize for an unfilled buck tag. A shotgun extended my range a bit, but I didn't push it. I think my longest shot was about 65 yards. I was always satisfied with shotgun performance as a result. In my defense there was only once in all the seasons I have used my Rem 1100 in a shotgun season where I had to pass on a buck that was too far out.
3) When you find a load that works, buy up as much of that lot you can afford and squirrel it away. There is a lot of lot-to-lot variability and what works for you this year, might not work next year. Having a known load you're satisfied with will save you a ton of money over the years. Some guys like to invest $200 a year in ammo and spend a few afternoons at the range. I like to take the slug gun out, fire a few to check the zero and then go hunting. I invest my Saturday afternoons in the woods scouting, not at the range.
Even though I'm not an archer anymore, I still hunt about the same up-close and personal way. I moved my hunting to Kentucky years ago, and mostly hunt with rifles now. However, inside 50 yards, I would put a well-placed 12 GA slug on a par with a 30-06. I still try and get out with my 1100 one day year in Kentucky and hunt off the ground:
The Shaman's Myth of the Brush Gun-- the real one
You're right in the end: the brush gun is really just a myth. On the other hand, I can pick up my 1100 and a fresh box of Sluggers and walk into the cedars and something magical happens. The deer are sniggering as much as ever, but for one brief Saturday afternoon I'm away from the shaving mirror and me and the brush gun can slip into the woods. I can stalk the deer and when I look down that 1100 is still as bright and shiny as the day I bought it. The Remington Sluggers are just as green, and as long as I stay along the ridge, and maybe angle downhill a little bit and don't try to go back it can be like twenty-something years ago back in Hocking Hills on Opening Day. The only thing missing is the stray shots zipping through the tree tops. Those I don't miss at all.
Of course the 1100 is starting to get a little dented, but I'm not wearing my reading glasses. I don't see the wear on the stock, or the lines on my hands. Along about sunset, I start trudging back up the ridge and as long as I do it slow enough the myth keeps working. Finally, I get back home, and put my brush gun up on the rack next to Moose's Garand and Angus' Mosin Nagant-- my sons don't seem to mind the weight. They'd schlep a boat anchor through the woods if they thought it would get them a deer.
Once in a great while I catch some deer laughing a little to hard or too long out there in the cedars, and it makes the trip worthwhile by reaffirming the myth and topping off the freezer. KY rifle season ends, and I don't feel bad about not buying an Ohio tag and joining the orange army the next Monday for the start of shotgun season. I put the 1100 away and don't think about it until next year.