I am a mono user, for 30 years and a whole lot of animals. I like the TTSX, but would absolutely use an LRX if I felt there was an advantage at the ranges I shoot which are pretty much your self-imposed ranges. I like to go a weight or two lower with the monos, the 110 TTSX is where I hang my hat for the 270 Win.
A 270 Win at point-blank range (60') with a 110 TTSX at 3350 fps mv straight into the sternum of a lead cow elk says it does alright. Nose dived at a trot into the snow and that was it. Didn't find any bullet/petals in the animal, but it was a 0 deg night and wasn't looking during field dressing. Heart/damage was noticed, undoubtedly contributed to by the sternum shrapnel.
My understanding of the LRX is petals shearing off at shorter range but past 100 yds haven't heard much different than a standard TTSX at the ranges you are looking to shoot. Petals coming off is not a negative with respect to internal damage.
I would use either one, whichever shoots best or is available if you choose the 130 gr class of bullets.