Your Globals are sharpened to a 15* edge angle on each side. That's a 30* included angle, FYI. The Furi sharpens (if you can call it that) to a 20* edge angle (40* included) As you can see, it's a more obtuse angle than the knife is made for. The obtuse angle itself won't make the knife duller, but it will make it ACT duller, and go shorter between sharpenings, too.
I'm not sure if "ruin" is the right word or not. The Furi sharpener is a poor system for any knife, worse for yours. Globals aren't exactly the top performers of the knife world anymore, but they're darn decent knives and are worth maintaining in the way they'll work best.
Getting back to the magic fingers of Furk: They are pretty easy to use in terms of having a low learning curve, and those who made the gift to you may have been impressed by having knives that were even half sharp as a result of their own efforts. Getting knives sharper than they were, in the privacy of your own kitchen, is something which escapes most modern people. It's empowering when it happens.
Oddly, there's no such thing as a "super-pro" edge. Many (actually probably "most" by a large margin) professional chefs and cooks don't have the foggiest concept of how to sharpen a knife well themselves; and seldom if ever use knives which are actually sharp.
As a home cook, just like a pro, you want to sharpen a knive until it's "very to extremely" sharp, and resharpen it when it becomes merely sharp. In your own words, as a "keen home cook," you should have a keen knife always. In my opinion sharpening is part of good technique for the home cook.
The easiest way to do that is with a Chef's Choice (electric) sharpening machine. Chef's Choice makes sharpeners in the "Asian" 15* angle that would be fine for your Globals and sell them for less than $100 USD. A lot of old timers have the mind set that machines will hurt your knives. Used properly, a Chef's Choice will do less damage than almost any alternative; and far, far less than a system like your Furi.
Other good methods are learning to "freehand" sharpen on whetstones (either oilstones or waterstones), and a "rod-guide" system such as the EdgePro Apex.
As do most "knife" people, I use stones, freehand. However, it is a skill which requires a skill (not that it's all that hard), and a good stone kit does end up expensive. The strengths of the method are that once you've mastered the skill, you can sharpen practically anything; and you can learn to do it at a very high level indeed.
Rod-guides are much simpler to learn, but are a bit of a PITA. Also, the good ones are expensive. You're looking at something more than $150 going in.
Less good but less expensive, are the "slot guide" manual sharpeners such as the Minosharp Global sells for its knife. They're a lot of work to take a knife from dull to sharp, and an enormous amount of work to do any sort of repairs. Everybody and their uncle make slot guides: Chef's Choice, Wusthof, and so on. Most of them are angled at 20* and are totally inappropriate. Of those with 15* angles, like the Minosharp and the MAC rollsharp ... well, not great.
The same is true for "V" stick systems such as the Spyderco Sharpmaker.
Neither the slot guide nor the "V" stick will provide anywhere near an appropriately fine edge. I guess you could say they're OK for "touchups," but not for real repair, sharpening or polishing.
A not inexpensive "V" stick alternative is the "Warthog," which actually is pretty good, efficient, versatile and so on. Not cheap, though.
In addition to a good sharpening system, you'll want a good "steel." The steels that Global packages with its sets is too rough to be very good. I suggest a fine (as opposed to coarse or medium) ceramic, like the Idahone 10" fine (under $25 USD).
I've tried it. Not to be harsh, but no Furi knife or sharpener is any good.
Sorry to be the bearer of bad tidings, don't shoot the messenger.
Hope it helps,