I personally would say that a 3' is "definitely" too small for an average beardie. Having had to keep an adult female (only 18") in a 3' for a week whilst I was adding some extra vivs on top of her cage, I would advise people not to keep a beardie in there full time. It looked far too small and cramped for her, and whenever she tried to run or do anything other than plod around she quickly hit the other end of the cage. An extra foot may not sound like much, but it's almost double the effective running distance for her (assuming she's 18", she has 18" to run in a 3', compared with 30" in a 4')
Have you considered Rankins dragons? They typically grow smaller than a beardie, and should be ok in a 3' as adults.
With regards to the MVB, I personally wouldn't touch one without a stat, especially not during the summer. They definitely have higher UV output, but there is the safety issue; they must be mounted further away from the animals to avoid overexposure to the UV, and they can pump out a fair bit of heat. I would definitely say a 3' is too small for one; it would be extremely hard to get the temperature gradients etc.
Have a read through
UV Guide UK - Ultraviolet Light for Reptiles - UVB reptile lighting on test; they have tested out various MVBs and tubes; a correctly set up ReptiSun 10.0, mounted on the backwall with a reflector will give you a similar UV output much more conveniently in a smaller cage, with the added safety of being able to use a dimmer stat with it. It will also cover the entire cage, rather than just the basking spot. If the basking spot gets too hot (which it may well do with an MVB in a low cage), the dragon will sit around the periphery of the actual spot to bask. Due to the UV profile of an average MVB (again, see uvguide.co.uk), there won't be much UV around the edges of the basking spot, so the "advantage" of using an MVB for the higher UV is lost.