That is exactly what I was thinking. I recently got a 60's model Traynor Bass Mate head (EL84 version). Stock, it's actually got a lot of that characteristic Dr. Z. EL84 tone. More so then any other EL84 amp I have tried. First time I used it with a Tele, that Dr. Z sound is exactly what came to mind. As other said, not the exact same but at well less than half the price pretty darn good.If you can find a good vintage used Traynor amp or blackface Fender (like Bassman) it might be a little cheaper and still have some of the character and quality construction of a Dr. Z. Also depends which Z you like. If it is one of his lower-wattage EL-84 models, maybe look for a similarly configured old Traynor, like a Bassmate for $300-400.
Not saying these will sound just like a Dr. Z, but these are some of the lower-priced amps that will give you some of those sought-after features.