FiveBlues - Welcome to the forum -
I wanted to chime in here since I actually grew up with a pair of Snells and I'm quite familiar with the sound.
These were my dad's that he powered with separate preamp and amp made by a company called Amber. Unlike yours, his were the Type E II from the mid-80s and had a second rear-firing tweeter.
I remember distinctly that the Snells had several things that worked against them - the cabinets were lightweight and poorly damped leading to a lot of coloration and that the imaging was also very strange and the sound not at all dynamic or realistic.
This is all, of course, just my personal opinion so take that with a grain of salt if the Snells are something that you really enjoy.
As far as recommending other brands of speakers that will fit in well with your current Snells, that would be difficult as I've yet to hear anything since then that sounded similar. If you're committed to the brand and want to do a 5 channel setup, I would use one of your existing speakers as a center and then try to hunt down 2 pairs of the larger Snells (like the Type E's I mentioned above) for your main L-R and Surround L-R.
Interestingly enough, I think that the rear-firing tweeter might by fun to try for a rear surround.
As far as recommending another brand in your budget (assuming you want to start from scratch), that's a bit tougher since it all comes down to the sound that you're after - You mention that you would prefer to stay with something within the same quality/ sound as the Snells, but I think that would be difficult as there has been quite a bit of advancement in cabinet, driver and crossover design since the 80s.
Maybe you should go give some other speaker brands a listen and see what suits you, otherwise, if you're patient I'll be you could eventually source a complete set of Snells well within your budget.
As a side note, my dad ultimately let go of the Snells and went with a set of Vandersteen 2Ce's (lots of bang for the buck) and has been very happy with them. These routinely can be found easily for under $1K / pair and are a huge step up in performance from the Snells in every respect.
Perhaps you could check them out and see what you think?
Greg