The Adcom GFA-555 (and Mk II) works great with RS-IIIa's, sounds excellent, is nearly bulletproof, and would fit your budget quite nicely leaving some extra for music or cables...or the next piece of gear. I used a Mk II on my RS-IIIb's for many years, and it did an excellent job...smooth on top, with excellent bass control, punch, definition, and extension.
Or if you can be patient, look for a Forte Model 3 or Model 6. Forte was a 'budget' line made by Threshold, but there's nothing budget about the design, components or build of these amps. The Model 3 was designed by Nelson Pass, the Model 6 by Jon Soderburg (IIRC). I've got two Model 3's bi-amping my RS-IIb's, and a Model 6 driving a pair of RS-IIIb's.