You need a decent amount of tension for the string not to be floppy. If you understand the Physics of how string instruments work (I studied precisely this stuff in college), the formula for string gauges with the same tension across the strings falls out of the Physics. Unfortunately, most folks seem to like an arithmetic progression for string diameters - 40,60, 80, 100, 120. That sounds like a nice progression, but it doesn't work in practice. The notes of a musical scale are a geometric progression, where the change between notes is a ratio, an instrument tuned in 4ths also follows this rule - for constant tension, the frequency ratio is 3/4 as you go down, the diameters of the strings should go up by a ratio of 4/3. on the previously cited set, the G and E strings are about the same tension, the A has more tension, and the D has a bunch more tension - we're not starting in a great place, but it gets worse as you add a B string. If you like the tension of your 100 gauge E, the B should have a diameter of 133 (call it 135 as the closest multiple of 5). For a 105 E, you should have a 140 B. Now, take a look at 5 string sets - do they follow this progression? Nope. The B is much thinner - why? Good question. The answer to that aside, It's too skinny. Why is the B string on many 5's floppy? The string is too small. This isn't rocket science (it is Acoustical Physics)
Bass makers (you can ask around) tried to get string makers to make string sets with rational tension, but when that didn't happen, they made the scale longer - they figured that would at least help the worst string. That does help a bit (not enough actually), but it also raises the tension of the other 4 strings. Your D string, which already had too much tension, just became more of a problem. Not much progress has been made.
A longer neck also makes it floppier - if you want a stiff neck, you don't want to make it longer. All you need to so to understand this is walk out on a diving board - the further out you go, the floppier it gets. The bass (as a solid platform for the string to vibrate on) isn't getting better as it gets longer, it's getting worse. A 34 with the right gauge string is actually better than a 35 - that's the Physics of the situation.
So, applying the science to the situation, it's a string problem. The best place to fix a a problem is at the source of the problem - the right strings (that's my Engineer side talking).