I didn't know the Sire 5 strings were 35" scale. Good info.The new Sire M7 five-string has a 35" scale length. I have one arriving in about 2 weeks. It is not "inexpensive" but not expensive either, at $699. That looks to be a phenomenal bass with the Marcus pre-, selectable series/parallel/humbuck pickups, flame maple top, adjustable string spacing, and so on. My expectation, having researched it a bit, is that it'll be approximately comparable (but with better pickup options and preamp) to a MTD Kingston in quality, which go for about $1300 new. So, better than a MTD Kingston, not as good as an MTD. Pretty good niche to be in for a $700 bass.
That's a little higher than the OPs range, but not by much. The reviews of Sire have have glowing. If I decide to get a jazz bass, that's where I will go.