With the diff cover off and the Trak-Loc housing with its open side to you as you're looking at it, you should be able to see how much play you have (with the tire and brake rotor removed, laying on your back, you'll be able to stretch your leg and work an axle shaft back and forth).
Also, if you just remove the cross pin, you'll be able to up close inspect it to see if there's any wear on the pin. If there's none or slight, then the axle shaft ends wouldn't be harmed in any way - there'd be no contact to cause it.
When I installed the Richmond Gear axles in my Town Car, they were actually just a tad too long and had to touch the ends with a grinder to be able to install the cross pin and C-clips. But I still have about 3/32 - 1/8 of end play. Never been an issue.
2005 Lincoln Town Car Signature Limited
5.4 liter throttle body; PI oil cooler, intake tube & air box; Mark VIII aluminum driveshaft; Trac-Lok limited slip; Richmond Gear axle shafts; J-Mod with Sonnax valves; Limo rear control arms and a great sounding stereo that won't ever automatically remember my Bluetooth settings
1999 Mercury Grand Marquis (gave that to youngest son, and he's now a converted true believer)