Okay, I will stick my nose in and say what I know.
I have probably twelve or fifteen el-cheapo ten-dollar (five-dollars on sale) Harbor Freight "float"-chargers for the last several years with absolutely nothing but GOOD to say about them.
I use them constantly and have NEVER had one to fail.
Multiple batteries makes no difference to a single "tender" as the tender sees the voltage as being only one battery, regardless whether there may actually be a dozen.
Before ever having the "tenders", I had to replace mower batteries every year; now I am going on past five years on the same batteries and the mowers can sit un-used all winter and still crank over like new.
With several seldom driven vehicles sitting around, mowing day was always started by jump-starting a dozen various vehicles just to move them around; not any more !!!

with the tenders always connected they crank over with authority and keep cranking until the engine fires; that alone is enough to convince me of their usefulness.
All of that being said, I tend to think that your problem may very well be the tender you are using.
Humor me and try a couple of the ones like I use and see if that doesn't cure your problem.
If it doesn't, and the truck keeps killing batteries, then you have some weird electrical issue going on, possibly within the regulator of the Leece-Neville.
Is the Leece-Neville a 110-555 ??
If so, it is a five minute job to swap regulators.
But then, it IS a Leece-Neville, so I doubt it is the culprit.
