You have the ECI open reach modem and it should work fine but the model I am referring to is the Openreach Huawei Echolife HG612 version 3B which is much easier to unlock.
I would leave the open reach modem in place and this will take over from the built in modem in the HH5.
I take it you would prefer to drop a little in speed but gain a reliable connection and with it in place things should be better unless you have an issue on your telephone line.
I don't see any difference in my speeds with the Huawei Echolife HG612 modem connected to the HH5 or not but after the recent firmware update to fix connection issues I did notice a sudden change in my HH5 and it not connecting after only a couple of days and this was not the case before the update so I have opted to connect the modem once again and all is well again.
I've put the openreach modem in it's place for now, I'll keep it there until further notice as I was experiencing a few drops earlier with the HH5 modem and what not.
Will report back and let you know how it goes within the day.