Your biggest problem is the water. An additional pitfall is the size of your recipe -- which is on the large side. However, the size problem will resolve itself when you stiffen the custard sufficiently. Cut out the water; bump your milk quantity to 1-3/4 cups total. bump the flour to 5 tbs total -- that should be plenty.
Just forget the "thin syrup" thing. You don't need to make caramel for butter scotch, it's enough to dissolve the brown sugar.
Instead of your previous procedure, mix the dry ingredients in the top of a double boiler, then slowly add the milk and cream, and cook, over boiling water, stir often and cook until it thickens. Reduce the heat so the water in the double boiler is at a simmer. Cover the custard and let it cook for about ten minutes more.
Meanwhile beat the egg yolks.
After the ten minute cooking period has elapsed, remove the cover and stir the milk mixture. Pour off about about 1/2 cup of the cooked milk mixture into a measuring cup or small pitcher. Slowly add it into the eggs, whisking all the while to temper the eggs.
When the egg mixture is tempered, add it to the remaining hot milk mixture and cook (still over simmering water), stirring constantly, for another 1-1/2 minutes. Remove the top of the double boiler from the from the bottom, and set it on your counter.
Cut the butter into a few pieces, add them to the custard and stir them in. When they're fully incorporated, add the vanilla.
Let the custard cool -- at minimum until the side of the pan no longer feels hot to your hand -- and pour into your pie shell.
Make the meringue, top the pie with it, and finish as before.
Changing out the water, and cooking in a way which maximizes thickening should stiffen the custard considerably. However, butterscotch pie is never any stiffer than a stiff pudding -- because that's what it is. You'll have to reconcile yourself to its limitations.
Please let me know how this works for you.