Advice on best mid priced MM cartridge choice for Rega P3 (2016)

I'll second the hana eh recommendation. I use the el version and it is lovely. 

If trying high output MC, like Hana EL, directly into MM Phono, it's still only 2mv. 

IF you have any hum when you turn your phono/preamp/amp volume up, I suggest sticking with MM as OP wants to do.

Thank you all for your input, I really appreciate it!
My reasons for potentially choosing one of these four cartridges are price and accessibility.

My system is modest, so regarding price I’d prefer to stay under $500. $350-$450 would be the sweet spot. I’ve heard the Ortofon 2M Blue and Nagaoka MP-110 on other turntables, of the two I liked the Nagaoka better.

But I like the way the Ortofon mounts better than the Nagaoka carts, with the top screws. So my hope is to learn from someone with a Rega 330 tone arm who has actually experienced these carts. Maybe the Bronze would sound great on it, or maybe the Nagaoka is a better choice? I have no experience with the AT or Sumiko carts.

I have not had hum issues thankfully, I use the phono stage built into my Marantz PM KI Ruby integrated, and it seems solid. As a relative newcomer to this hobby, it is quite helpful to learn from all your experiences-thank you for your generosity to share what you have learned!

I have a Rega Planar 3 with groovetracer mods and the Hana SL cartridge is amazing with it.  I'm sure their MM cartridges would work equally as well.  A 2mm shim was all that was required.

There is only one cartridge here that has an actual return policy. A policy that says, if you don't like it, return it for a refund.

And that is the new Teo Audio MM CBP Cartridge. 

We believe in it enough that we don't think that anyone will return it.  Even if they normally use cartridges that cost 2-3-4-5-x times as much. Be they MM or MC in type.