I know sticking with Tesco is the granny option. A brand I know (although apart from phones I hardly use Tesco, I dislike them quite a lot as an entity but they suit me for simple phone stuff)
I just feel reassured by knowing I could go to my local branch/shop and complain until I got a problem sorted, rather than dealing with one of these other firms who are probably perfectly ok. Probably the same reason why when I wanted a tumble drier or a vacuum, I would use JL rather than a slightly cheaper internet shop, IKWIM.
Or even keep the PAYG as an emergency/spare... really depends if it is locked to any network as to how easy it would be to sell... and if not locked, then at end of contract, use PAC to keep your number and then get a fresh SIM Only to keep the Nexus running.
The PAYG could be used for a week/two on <any other network> then you get a PAC from them and go back to Three (also if you buy the SIM Only via a cashback deal... you're a new customer on Three at that point... though must admit some other networks are more generous on cashback deals).
CLEARLY you must check what coverage there is from Three in the areas you are most. Was serious when I mentioned Wales as lots of areas will have poor/no coverage.
My sister can only talk to me when walking on the beach at Anglesey, or from one spot by a door in their cottage. I just send her texts these days or ring their landline as there's little guarantee of reaching her on Vodafone (though you mentioned them yourself... so Asda Mobile would be no good as a PAYG intermediary!)
O2 sim only £10 pm which they double up if you pay DD. plenty of minutes data and texts there for the light user. As you say, good coverage too. Phone wise ANYTHING with a good sized screen and running jelly bean as a minimum.