use to call this ol guy on the phone and he would hold me hostage reciting all these transformer tidbits from memory, so i would write them down,
compiled the notes in the pic below,
one thing he said was the LS-10X had the same lams as the smaller A-10, it was just a bunch of nested shield cans in a big case,
i never hacked one so no first hand experience,
if it is the 31 UI lam, then you can calculate the flux, as it probably has the same tuns as the A-10, which is 8800 turns of #43
https://img1.wsimg.com/blobby/go/0e07cc59-2f5a-481f-967d-12c7363b86fa/downloads/1ctumb47q_789019.png?ver=1566021456329
a 0.39" stack of 31 UI at 8800 turns = 4.3. KGauss, nickel will take 5 KG before saturation,
max input voltage on the pri side will = ten times that on the secondary, so that transformer will take 24 volts on the secondary if used backwards, certainly enough headroom to be used as an output, but your signal will be stepped down 10:1 instead of 4:1 for your typical tube output rig, but you can amplify that,
what about the increased current on the secondary over what it usually sees?
DCR will save you there, secondary DCR on A-10 is 1600 per coil, so 3200 series.
24 volts / 3200 = 7.5 ma, #43 is speced at 4.8 ma, which can usually be doubled or tripled, so yes, you can use the LS-10X as an output transformer and it might sound very nice if it sounds anything like the A-10 used frontwards.
phase shift at 20 hz - 3200 DCR / 250 K XL @ 20 Hz = 0.0127 arc tan 0.0127 = 0.72 degrees, not bad.
(assume 2000 Henries sec ind @ 20 Hz)