I wouldn't do a great deal differently than they are now. Sure, I wouldn't have picked up the phone and called the Nasty Boys and asked them to report bright and early for work, but then again if Hogan was offering to come into the company and that was one of his conditions, I'd say sir, yes sir.
But the reason I wouldn't do much differently is that there is no magical quick fix that is going to instantly catapult their ratings and suck the life out of WWE. All they need to do is remain consistently in people's consciousness. It's all well and good putting everything you have into a pair of impact shows and getting a slightly higher rating than usual, but if you can't do it every night then it doesn't mean a whole lot. They need to still be here a year from now, hopefully still producing a live wrestling show, regardless of what night it's on. Most WWE fans now at least know TNA exists, which they may not have done as little as 2 years ago. I know a lot of my buddies didn't. That is definitely a positive start, but what needs to follow is reassurance that they are not a flash in the pan.
They need to have longevity and invest in their future to assure that this isn't an all-out blitz on WWE that burns them out within 6 months. They need to be looking at who their top players are going to be a year or more down the line. They need to be constantly scouting for young, athletic talent. They need to establish traditions and characteristics that make the company an alternative. An event like Lockdown is a great start. The Ultimate-X and King of the Mountain matches are also fantastic and don't need to be tweaked. They need to continue to make sure they give 110% for each Bound for Glory, because it will never be on the scale of Wrestlemania (neither was Starcade), but fans respond to "THE show".
Are veterans and short term surprises important? Yes, absolutely, name power is a vital part to the industry, so if an established wrestler becomes a free agent they need to do their best to snap them up, but at the same time they need to be investing in a youth movement year on year. By all means let Team 3D and Beer Money be the elite teams right now, because MCMG and Generation ME are years younger than them and will be there when they are gone (hopefully).
Guys like Jeff Hardy, Rob Van Dam, Kurt Angle, Sting, Hulk Hogan and Ric Flair are important because a new viewer will instantly recognize them and won't feel alienated. Whereas if you were switching from WWE to ROH for example you'd have almost no clue who any of them were and no compulsion to stick around and find out. TNA have some big name players and thus a safety net to catch their new viewers if they're feeling lost.
Given complete roster freedom I'd send home the Nasty Boys, Bubba the Love Sponge and Jimmy Hart, but realistically you can't give Hogan's friends their marching orders without the say-so of Hogan, and as many negatives as he brings, he brings more positives from where I sit. They have been instantly more recognizable since he came in, in spite of the at times questionable or at times downright ridiculous things that he's insisted upon bringing with him.
To sum up: Don't do anything drastic. Unless Randy Orton, John Cena and Chris Jericho all decide to up and leave WWE and sign with TNA, no single action is going to close the gap. It's going to take years, not weeks. It's going to take commitment to potential fans to assure them that they are the real deal, and not just a flavour of the month promotion that will be bust just as quickly as it gets good. TNA have done a good job of this so far; nobody ever believed in them and every year people say "I guarantee you they'll have folded by this time next year" and like them or not they have grown every single year since their inception. They should continue on the path they're on because it has worked thus far, and in my opinion it is foolish to go all-in with the hand they already have when they could just bide their time and slowly grow. I know Hogan's pride is on the line and they'd like to be able to achieve success while Kurt Angle is still an active performer who's name still matters in this industry, but they really do need to pick their spots and play the waiting game.
That being said, it was probably too early to move permanently to Monday nights, the audience for wrestling generally is far smaller than it once was and asking them to out-right choose isn't wise because if a gun was put to my head and I was demanded to only watch one forever more, I'd pick WWE, even if I do have major major love for TNA's roster. There are die-hards for each who are going to watch through good or bad, and there are those who are on the fence, willing to give both a chance. These are the people TNA need to try and tap in to, and to be honest the best they can hope for here is that they will watch both shows, and they can't do that if they're on at the same time.