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If it's really going to be a backup for your NTG3 (as in: will sit in a case unless your NTG3 goes down), why not a used NTG3? That'd match well, if continuity is a concern. And the NTG3 is a decent mic (as you know).
Interesting that Jason recommends an Ambient Tiny Mike/Mic (they seem to spell it both ways). I have one to and use it on cameras (with the Rycote mount, windshield, etc). It's pretty good and very small and light. I haven't compared to an NTG3, but it's an interesting idea. http://ambient.de/en/product/atm216/
IronDave here like the Diety S-Mic2. I haven't used (or even seen) one, but Dave seems like a smart guy. And they're inexpensive:
https://www.deitymic.com/smic2/
If the NTG3 is working everywhere for you, then another shotgun can be a fine choice. But if you want a mic more for interiors (or small close exteriors), maybe consider a used Audio-Techinica AT4053 or an Audix SCX1HC. Those are both nice for dialog, imo. I'm more familiar with the AT4053; it's underpraised imo.
That's about all I can think of in your price range. What do others recommend?