There is certainly a lot of support for going 6SN7 with the 6SE. I thought I'd throw out that there are still a few of us who haven't gone down that road (yet) and we're finding good results with other options.
Instead of getting the 6SN7 adapters I opted for the 6DN7 adapter. I've been pretty pleased with the results, especially with the HE5-LE.
I also acquired the 6EM7adapters from Jack but honestly I've not been able to give them much head time except for a brief audition when they arrived... which seemed promising. It reminds me that I need to get them back in the amp!
And of course I'm still a fan of the good old Sylvania fat bottle black plate 6FD7's!
I've also recently started listening to more rectifiers since getting a 5Z3 to 5U4 adapter.