Hi there!
We're literally in exactly the same situation as you - though, perhaps slightly further along as we're due to complete on a place in the next month or so. Same experience - like the town centre, decent transport connections, great houses, good schools, plenty of restaurants, decent pubs, cinema, one of the oldest street markets in the country, theatre etc. There's even Enfield Dairy, to replace our milk delivery.
Also love the fact that we have so many great parks, Forty Hall, and Capel Manor gardens on the doorstep. It's a complete mystery to us why similar houses in Leyton go for £200,000 more. Fully expect this to change when the new trains arrive on the Enfield to Liverpool St line this year, and stations receive further additional investment.
We're in the catchment for George Spicer and Raglan. We still have to visit them, but they seem like really nice school communities. GS isn't Outstanding, but Good is perfectly o.k for us as long as the children are happy; Enfield schools also seem to have more play space - Raglan has a massive field, and a very strong focus on sports and extracurricular activities. We're moving from an Outstanding, oversubscribed primary, with far less play space and no focus on sports, so we think we're gaining something on balance.
Appreciate this isn't exactly what you were looking for, but hope it helps a little.
Good luck with the search!