I've considered purchasing a bass and modifying it to be a "Contrabass" but after thinking about it was dissuaded as I came up with the reality of multiple problem with an F#BEA-tuned bass. Some of what came to mind is that you oftentimes not only have to purchase a new bass
specifically designed around low tunings (woods that resonates at low frequencies well, specialized hardware such as tuning machines and bridges that can handle heavy gauge string sizes, pickups and electronic designed to reproduce the frequencies, etc...) but also purchase specialized sets of strings that are likely to be a good deal more expensive than "standard" strings (JustStrings.com has Warwick's Black Label Stainless Steel "[Invalid or Expired Link Removed]" F#BEA-tuned strings (.175, .135, .105, .085) for $48.35, more than
3X my personal 4-string set o' choice, D'addario ProSteels EPS170 .100-.045) as well the reality of little choice should you not like the tone of the steel "Dark Lord" strings AFAIK there's no string set close to the same gauges as Warwick's, unless you can get a string manufacturer to make a custom set, which I imagine would still have the problem of high cost-per-set.
The other major issue is that for a bass with a tuning any lower than your typical AEADG (standard 5-string tuning with a "dropped A" for those of us with Hipshot Bass Xtenders on their B-strings) I would think that you'd have to invest in an
expensive amount of new amplifiers and speaker cabinets that are also specifically designed to be able to reproduce said lower frequencies. Because cabinets that are more "stoutly" designed and built reproduce lower notes better (I once read a comment by a well-known Bass Amp and Speaker builder than the *ideal* material to use in a cabinet for bass reproduction would be "Concrete"

), said cabs are likely to be a good deal
heavier than most on the market when one of the main selling points currently is the
exact opposite: *lighter*, 1 or 2 Neo driver cabinets that are easy and quick for load-ins and outs. You read in the Amp forum about players gigging with a 1x12" these days... I'm no expert, but I imagine that you'd need a HUGE increase in both overall speaker area as well as a dedicated sub with a X-over to remove all of the high range from those speakers... in the end, a stage rig that would be more akin to an arena stage than a club. And I'm not even
addressing the dirty looks and outright "No"s you'd be likely to get from people working Sound and how the average venue's Front-Of-House sound wouldn't be close to be able to duplicate your unique rig...
...but to answer the OP's question about 4-string basses designed for lowered tunings, I agree that the main ingredient is an increase in scale length and that the best bass on the market for a reasonable cost would be the Spector Euro LX 4-35, which Colin Edwin of Porcupine Tree used on their tour for numerous songs off their then-latest CD "Fear Of A Blank Planet" that were tuned C/F/Bb/Eb and was quoted as saying
"The [Invalid or Expired Link Removed] has a graphite-reinforced neck, which means it can come out of a freezing-cold trailer into a hot gig every night for a month without going out of tune or having any trussrod problems" and which he's also used during the sessions for their upcoming album "The Incident". However, for a great
budget bass I'd recommend the
Link Removed (
*not* the lesser 34"-scale
374 model, which was a lower-priced replacement). I owned 2 of the 775 5-strings, a fretted and converted fretless, and was very impressed in the build quality, pickups and sound, and tension from the 35" scale. In a Shootout of "4-string Basses Under $800" in Bass Player, the 774 was chosen as a "Best Buy" and given high marks on it's overall quality and tone. They were sold for a song after Yamaha discontinued the line (I got each of mine for just over the price of an SX when they originally went for around
$700 apiece

) and were great basses that I used for about 4 years solid and led me farther down the path of Jazz-esque basses.