My RF EE friend says that this project should be very simple, which is exactly what I thought when I started it! He advised not to use the LimeSDR but to go back to basic hardware, making sure that the amp components were very 'linear' for LTE use. I am trying hardware options as well, I'm not sure what his drinking/eating habits are yet, but rest assured there will be some kind of homemade product to reward him with.

There's probably something very simple that's wrong with my set up, but like diagnosing fuel starvation problems in diesel engines, just looking for leaking diesel is not the correct approach.

Upgrading my iPhone has helped a lot as it can actually receive 4G in my location - very useful! Much easier to spot it on the spectrograph:

I'm having a go at building some alternative duplex filters from scratch - they're the most obvious candidate for troubleshooting at the moment - there seems to be quite a bit of noise generated and a lot of signal strength lost by using the current ones.