I have recently struggled to get a Z3C operating with EE (best coverage 4G, first 5G) in the UK. My travails sounded very like yours. Fortunately, I had a really helpful Meraki support engineer - Connor Loughlin - in London. He went out and got an EE SIM and then confirmed that the EE network functioned with Meraki devices, without using ASNs.
The problem was that the picture beneath the Z3C's SIM slot of a stylised SIM encouraged one to insert the SIM wrong side up and wrong way round.
This photograph shows the correct SIM orientation and is now in the Meraki support notes -
The other problem was really dysfunctional systems at EE. As the LTE connection is predominantly for odd situations where a wired connection is not available, PAYG made sense; it transpires that in this situation one has to put a credit on the "My EE" account and then telephone an EE support person. The support person transfers the required amount from one's My EE account to the PAYG data SIM account. This prompts much eye-rolling but works. Again everybody was polite and helpful, but the subtext was, that I'd find it more convenient to transfer my mobile phone to EE.
HTH