BEAD tuning is not going to put any extra tension on your neck if you do it right. In fact if you were just to down tune a standard four string set your tension would be a lot less and you would have very floppy strings. So what you could do is move the E, A, & D strings up one slot in the nut (which typically requires some filing) and tune them to their natural pitches which will put them each at exactly the same tension they were at before. Then you just find a B string that matches the tension of your E string, except that you are going to find that common B strings are a bit looser than common E strings. So you will almost certainly end up with less tension and no concern over the strength of your neck. What people commonly do is to buy a 5 string set and throw away the G string and this will also get you close to the same tension you had before if the gauges of the E, A, D strings are the same you had before.
Or you can look at the D'Addario and Circle K Strings tension charts and choose string gauges that put the tension anywhere you like. Circle K Strings
and Bass Strings Online
will both sell you single strings so you can put together custom string sets that will give you any total tension and any string by string tension that you want at a reasonable cost. There is absolutely no reason to worry about tension if you want to try a non-standard tuning, just do the math and order the appropriate strings. On a 34 inch bass anyway, other scale lengths have limited string choices compared to 34 inches no matter what their proponents may try to tell you.