I use the Selway longbow stringer and have had good luck with it. I do leatherwork as a hobby and have also made the "cup-type" stringers and have used them.
The longbow stringer does get used on my recurves occasionally and it works, but I have a dedicated recurve stringer that works better, as it holds the string on the tip more firmly. Other than that they are nearly identical in practical use.
I do use the "push-pull" method occasionally, but as a rule I use a stringer on my bows.
The Boy Scouts at one time taught the "step through" and the "push-pull" methods, but no longer (that is what I learned a long time ago in a galaxy far, far away). I am guessing they were deemed potentially unsafe or the potential damage to a bow and/or Scout is too great.
The Archery Merit Badge now states "Always use a bow stringer when stringing your bow. Improper stringing or using the step-through or push-pull methods can cause permanent damage." The manual makes no differentiation between a longbow and a recurve bow, as far as stringing the bow is concerned.
The Selway stringer can be purchased from a number of different sponsors of TradGang.
RonP