Integrated Amp Bargains with good balanced sound?

Two integrateds I would recommend in that price range are the Audio Refinement Complete, which might take awhile to find used, and the Onkyo A-9555, which you could buy new for $500.

I'll second the Audio Refinement integrated suggestion. The NAD C370 and C372 also warrant investigating.

My personal favorite (at just slightly above your budget) is the Vista Audio i84. I've mentioned this unit before at these boards, and while I should practice keeping my mouth shut - this is a unit I wish more people could hear. I've got it setting next to Lamm / McIntosh / Lector gear and it's NOT embarrassed to be in this company.

Couldn’t agree more with the Audio Refinement Complete. However, since you mention a Rega P3 as part of your system, as far as I know, the Complete does not have a phono stage (or am I mistaken guys?).
A good match with your Sonus loudspeakers would be Unison Unico (hybrid integrated sporting 2 ECC82) that has an internally switchable MM/MC phono input. You might find one if you could spend an additional $100 or so. Otherwise, there is the less powerful Unison Unico P (also hybrid with 1 ECC82, 50 Wpc/8 Ohm against 80 Wpc for the Unico), whereby the plain Unico is undoubtedly superior to the "P".
Good luck!

To be sure: the phono stage is optional in the plain Unico, so make sure it has that option should you contemplate any offers! (It comes customarily in the "P" though)