I checked the 86 and 92 manuals and found nothing about checking the belt tensioner spring force.  If the belt length wear indicators on the tensioner are in range, the belt tension is suppose to be good (assuming I read the manuals correct this time).  My 86 5.0 with ~200k milage is still working good with the original tensioner spring.  Of course this is just one data point and your tensioner history is probably different. 
 
Guesses at cause and solutions:
New belt that has not seated in yet - may fix itself.
Contamination on belt - clean belt.
The new larger alternator is being spun too fast - larger alternator pulley (need longer belt for this).
 
That 6G alternator is a nice upgrade.  Good luck with the problem.

I swapped pulleys today. I will see if that helps. I got the alternator nut as tight as I could but not as tight as I wanted too. I need to borrow an impact wrench and do that thick cloth glove and impact wrench thingie....

You're making me reminisce about Renz (and probably Pratt and others) at Grandpa Skow's old Allis Chalmers dealership who would hold the alternator pulley with a thick cloth glove and hammer away on the nut with an impact wrench. And generators too. They'd fix stuff going way back to the WC days.....


Anyway, I was fooling with a belt tension gauge this morning and discovered that the gauge only goes up to 50 lbs and both belts are way above that. So a Pintkurstang is a way different animal than the Siemens ElectroCom DBCS994.... Even with that pesky DIOSS or CIOSS upgrade.... 


I did take a torque wrench to the AC and Alternator tensioners this morning. It takes about 15 ft-lbs more to move the AC side, so I'm guessing that it's Saint Henry's way of telling me that the alternator tensioner is all worn and wimpy.


Anyway, I've just bought a NOS replacement with pulley off eBay for $45.


Since the lower outlet on the radiator started leaking, that's been pulled and in the shop. And when it goes back in, I'm 99% likely to replace my no-name electric fan with an 8-blade thermo-clutch fan out of an '80s-'90s Ranger. I picked that up for $5 at a swap meet two or three (or maybe more) years ago for just in case.