Some rheostats (usually the better ones) have a bypass position; others still have turn or two of resistance wire in circuit even when all the way up. Easy to check, with an ohmmeter or by just opening the thing up and physically looking. Also easy to correct; a bypass switch and wire to connect it ought to cost about $2.75 at Radio Shack...
That done, if you can get mercury vapor lamps that aren't filtered or phosphor coated, they ought to work pretty well for contact printing with this kind of printer -- as a bonus, you can button it up tightly and not have to wear goggles while you print. The downside is the extremely slow startup time for most of the mercury lamps I've seen -- don't know specifically on the self-ballasting ones, but street and yard lighting used to be pretty heavily mercury vapor, before sodium lamps came along, and I recall that when turned off, they had to be allowed to cool for a prolonged period and then took 2-3 minutes to come up to full intensity after restarting (which itself sometimes took most of a minute).
An alternative that's likely to be cheaper, if slower, would be compact fluorescent (aka spiral) BLB lamps. They come in 13, 20, and 27 W ratings, start up in a few seconds and if broadly temperature controlled (say, kept between 70F and 100F) give pretty steady light after that first startup flicker. I've been using *one* 13W in a floodlamp reflector, about 8-10 inches from the print, and can make a VDB print in under 10 minutes with most of my negatives. No idea if platinum is faster or slower, but it should be easy to find out.