Just my thoughts, and you will of course have your own preferences:
Yes, the large-sized Minkus binders are truly awful. I have two of them as supplementary albums I picked up somewhere. They go with my Scott International albums (35 at latest count. Yes, it's an addiction.) But I cannot pick them up with one hand, and it's not always easy with two hands. Dropping a binder full of pages would be very unpleasant and, at that weight, it could easily damage the binder. I've seen enough damaged binders to know it happens a lot. The massive number of pages makes the pages curve so much it's hard to mount stamps and easy for them to fall off the pages. It's not a good look. Flatter pages are better. The same goes, by the way, for the large-sized Scott International binders. I have no idea who buys these gigantic things, but good luck! I suppose it's to save money, but if it makes working with your collection more difficult, is it worth it? I prefer medium-sized (2-2.5") binders, mabye 3" but no bigger, that I can pick up and which don't hold too many pages so the pages don't curve as much.
2-1/4" Scott Universal binders: I tried these and did not like them. They have a completely flat spine which I dislike the look of (the same for the Minkus binders with flat spines). They're cheaper to make that way, but most earlier binders and most higher-end binders today use a curved spine which I think looks much better. And it's easier to hold in your hand. Universal binders have a complex page mounting system you adjust for different hole punches, but it's not my favorite. The resulting album disappointed me mainly because pages don't lie anywhere near flat, but are extremely curved. This makes mounting stamps more difficult and stamps don't stay in place as well on pages that are that curved. Putting fewer pages in each binder might help, so might be worth trying. I gave up on them just like I gave up on the gigantic binders.
This won't help you, but for my Scott International pages I found some unused older Subway Stamp Shop binders which were copies of the Scott International binders, but better made. Subway sold them in various widths, and these are 2.5" wide which is absolutely perfect for me. So that's my ideal width. I don't fill them all the way, so the pages move around enough so they don't curve too much. It's the best solution I've found. They aren't sold anymore (naturally!).
A Minkus alternative might be the 2.5" two-post Minkus binder in this thread. I'd try one and see what you think.. But . . . these binders still retain the 2-post page-holding system which is laborious to use when you want to add or remove pages. I've got page moving down to a science, so for me it goes pretty quickly, but it's not as easy as it is in a ring binder. But a ring binder also doesn't always look very good and the rings are infamous for ripping the holes over time.
I'm not a fan of three-ring binders. They look cheap and don't work well. Large three-ring binders look like warehouse receipt storage binders, not stamp albums. If I used ring binders I'd use small to medium-sized ones and just use more of them. And I'd definitely spend a little more money and get good ones that look like albums, not some kid's homework binder. Browse Amazon
and you'll find a few that aren't too expensive which will work well. They're often sold as photo album binders.
As for hole-punching, if you go this route, you only need to hole punch once. Either get a good strong three-hole punch and do it yourself which will take some time but isn't all that hard -- or take it to a print shop and have them do it for you. They'll be much faster and the holes will likely line up better that way.
What I'd do is a bit different, though. I'd buy 22-ring binders and hole punch the pages with a 22-hole punch. I've done this already with some small collections. The result looks really nice. Twenty-two hole punches are a bit hard to find, but I managed to get one. Twenty-two ring binders are very popular in Europe, so buying from the UK is the best option. Their advantages are that they look a lot better than 3-ring binders, turning the pages is easier, and I find the rings don't tear at the hole nearly as much as they do on 3-ring pages. That's another concern for cheap ring binders -- they can tear the holes at least a little, sometimes a lot, which makes for a very messy album. This option clearly takes more effort and a little investment, but the result looks really nice.
Of all these options, the easiest is to pick up the smaller Minkus binders and move your pages. If you want to solve the problem easily and quickly, that's probably the way to go. You'll still have the two posts to deal with, but that's not so hard, and you'll solve your enormous binder problem. And look around as you may find them discounted somewhere. Good luck.