You have come to the right place to ask!
I have used the LT on 2 of my bikes and tried it on a third. The 2 bikes were a Yeah and a R20, and I was perfectly happy with the results. I used blue+black elastomers, a bit harder than the recommendation which I though too soft and bouncy when pedaling at my preferred cadence, 80-90.
I also put the TB once on my Downtube Mini which has a rubber doorstop in the back for suspension instead of the spring with which it came. Well, I hated it - way too much sway and movement. I would likewise never consider putting it on the Birdy, in fact I plan to get rid of the last one since I no longer have a bike for it.
So my own preference is definitely NO TB on a bike with built-in suspension.
(PS I still haven't put a rubber doorstop on the Birdy yet. Far too busy right now.)