herbejo,
L10468/VT22670 and LL1538 have almost the same ratio, but not quite, as L10468 has a slightly lower output, but not much.
Have you checked that the L10468 is correctly configured, the normal primary should be in parallel and secondary in series for ratio 1: 4.8, and then it is used backwards in the DI box as 4.8: 1.
I understand very well that the character is different, these two transformers have a completely different structure and material.
Another thing that is important to try is what the square wave response looks like, for example if you use 100 feet cable from the DI-Box XLR connector to the mixing console
1kHz square wave shall not have disturbing overshoot and ringing and not too much slope or rounding in its flanks, this will sounds like a big character difference between different transformers.
I have tried this carefully on the three transformers I recommend and which directly fit on the circuit board, LL1538 behaves extremely well on square wave and the other two very acceptable. (that's why I chose these three as different price options)
There are probably many other around 1: 5 ratio microphone transformers that fix good square wave response, like L10468, but I have not tested this myself.
--Bo