Hi Kim, a quick reply here as well. I've going to oversimplify things a bit to address the large model count issue.
I'm working on this myself, haven't field tested yet, but ran it across a tourney player who uses horde tactics. Also observing/hearing what's happening at least in my local meta, which is pretty competitive (because/despite they are very "flavour of the month" netlist-oriented, not the best way to play, but it tends to weed things out).
To take care of the shooty elements 1st, yeah, many Ork lists incorporate Mek Gunz (usually Smasha Guns) and Dakkajets now. Thus some shooty seems to always be relevant, I reckon many lists invest maybe 1/3 of their points in that area. So that's definitely tied to your interests, and happily easy to paint up!
Then that leaves the melee component, which is what I think you're concerned about because traditionally it means huge hordes. There seems to be 2 popular ways to go now. Either a Green Tide horde (huge mass or Orkz under the protection of a Mekboy Kustom Force Field) or Battlewagon Transported (which is the preferred Vehicle of choice now over all others it seems).
I think you'd be more interested in the Battlewagon method (to avoid painting up a huge Green Tide). You take Battlewagons with Deff Rollas, an upgrade that gives them a huge bonus to close combat. Fill it up with whatever you want to paint, the standard is Boyz, but honestly I think Meganobz or other options are just as good depending on the enemy and what you're willing to paint. I like to leave space for a Mekboy with a Kustom Force Field which will protect the Battlewagon.
Thus, I think a Battlewagon approach might be a realistic way to achieve what you want to do, you're still Orky without having to paint a huge horde. It's like at least a valid alternative to a Green Tide. The Battlewagon approach can further be enhanced by a new Specialist Detachment, Blitz Brigade, in the recent Vigilis book.
Not sure if this is what the rest of our Boyz on B&C are seeing, but I noticed suddenly people buying Battlewagons. I'm kinda doing a quick conversion on one of mine before I further commit, but I'm definitely building a Blitz Brigade or 2, as it might be one of the playstyles Orks can do that no one else can, and is also fun as a project.