Well, you have options. It really isn't necessary to narrow those options down is it? If you're willing to go the method that sacrifices the time and cost elements, you should end up with very close to what you're after in a short period of time.
I suggest you take it as a general project where you are 1) looking for the same color and era (60s keystone badge) Ludwigs; and 2) having a detailed "dream" vision of exactly the sizes you're looking for (Like the 22/13/16/JF configuration with 20/18/14hats cymbals, etc. Flat based cymbal stands, W&A snare stand, ec.
You're asking us to reduce your flexibility in getting your desired set together; but I'd suggest you keep that flexibility as a playing card on your search. In other words, you might find a reasonably-priced single rack tom or something, and then stumble on a complete set. You need flexibility to achieve the goal, so you're going to get the set then sell off the rack tom you bought or something, right? So, I'd suggest keeping your eyes open, and searching locally as well to see if you can't find a good deal somewhere where it isn't already globally marketed. You could luck out. If you're really reasonable and flexible you might be willing to even procure a same-era (and therefore same sound) set that is in a different color.
But Jonni's correct, they're available, just highly sought-after. This was the most popular color because of the Ringo connection but it is also the most sought-after too. It is the ideal collector's color because it is a beautiful color, they produced lots of them, AND many, many more than normal are looking for them as well.
Don't hold your breath, though. I stumbled on a few gems over the past 10 years or so, and they were great deals. But I'm hunting around quite a bit, and that is a long time to be looking.
When you consider the price they go for, and the price of a fine-quality brand new set, an original "Ringo" set might actually still be a reasonable value compared to say, a '59 sunburst Les Paul. For this reason, if you're serious about having some drums, and this is the only option, you could forgo the hunt altogether and just buy it from a reputable eBay seller or something at the current market value. If you want to you could run it by a forum member to see if we think it is really an original item and the seller isn't a flake or something. Then you could make the purchase of the drums minus the snare or even the entire set with the snare and buy the cymbals and stands or whatever--but it's probably going to cost you..
Like if you want to buy a rust bucket and restore it, or buy a pretty-good-original 67 chevelle. Same thing.. only different.
Lastly, I would worry about the non-original mods LAST, rather than FIRST. Those things are much easier to find and generally much cheaper and easier to add on, compared to finding those BOP Ludwigs. I'm more about the sound than the look so if it were me, I'd go for a different color and try to get some calfskin heads or whatever Ringo used on stage and in the studio to achieve that sound. Usually when I'm looking at a bass drum that is otherwise original and un-drilled, I will shy away from drilling it for a Rogers mount or whatever even if that's what Ringo (and other drummers in the 60s) did to their drums. I'm just more of a purist. That means refraining from drilling a perfectly-good 60s vintage drum. "Friends don't let friends drill." But once you get them, if that's what gets you off, they're your drums.. As long as you disclose honestly what you did to them when it comes time to selling.
