Go back to basics. The RPi1 doesn't really have the horsepower to show 1080p movies reliably especially over the network..
You need to find where the bottleneck is.
Use a fresh install of LE with no other addons or other detritus.
Use the same movie on NAS/USB/SD and see if there is any difference.
Use LE addons System-tools and NMON to monitor where the issue is, CPU, I/O, N/W.You can't say (as much as i hate to say this, this didnt happen on openelec) as you probably aren't using the same parameters i.e same setup, nor same movie.
Alot of things changed when the openelec to libreelec changes happened. I never noticed it when i play 800mb 1080p movies (torrented). But now im ripping ~2gig 1080p. I have started with a fresh install of Libreelec (previously it was a NOOBS install, now its a full on Libreelec install (not via NOOBS, using the libreelec easy installer.) But if the rpi1b doenst have the power well then im SOL 
but im going to order a rpi3 now and try then with that. But the NAS is the same, cables same, New SD card (high performance since i thought it was a corrupt card, it was me just using the wrong image) But ill start with the pi3 and see how it goes from there.
