I haven't analyzed the statistics, but based on the way you have those rules set up, I don't think you've made a significant change to the probability that Glitches will occur. And because of the excess ones causing hits to be cancelled, it seems like it would have the effect of causing glitches to be inherently worse and (also) more likely to be critical glitches.
Like I said, I haven't analyzed the statistics in-depth, and I don't plan to. But let me walk through a couple scenarios with this proposed system and compare it side-by-side with the core rules:
Scenario A (Original Glitch): Dice Pool of 13. Result: 7 1's, 3 hits.
Now, this fairly unlikely roll in the Core rules would be considered a glitch with 3 hits, which is a reasonably good success under most circumstances. If we were to apply your new rule, this (already) unlikely roll would have only a 1 in 6 chance of being a glitch, which technically reduces the chances of a glitch. If the "glitch" die doesn't roll a 1, then you're golden and all those 1's don't matter. Now, on the off-chance that you do roll that one on the glitch die, the results actually become rather dire. There are now 8 1's showing, which is five more than the number of hits. With your Hit cancellation, this means that not only did the rule make this a glitch, but now you only have 1 hit, downgrading that to barely a success at all. And if even 1 die had been different (1 less hit, or 1 more 1), the odds are significant that it would actually be a critical glitch instead.
Scenario B (Near Glitch): Dice Pool of 13. Result: 6 1's, 4 hits.
I see this come up a lot in my games, people roll just one or two 1s shy of glitch on their rolls and give that big sigh of relief, thankful that they didn't end up glitching. With your suggested rules, again, this result has a 1 in 6 chance of being a glitch. And again, if it does become a glitch, it means that the success is reduced.
Scenario C (Plain Failure): Dice Pool of 13. Result: 2 1's, 0 hits.
In the Core Rules, this result would be unfortunate, but nothing to write home about, there isn't nearly enough 1's to be a glitch (we need 7+, so even max Gremlins wouldn't do it), but there just aren't any hits so it's a fail. With these new rules, Again, there's a 1 in 6 chance of it becoming a glitch, and even more so, it would be a Critical Glitch! Even if there was a single hit, the new rules would ruin that simple poor roll into a Critical Failure.
Honestly, I like the idea of there being that fudge die to have a chance of pushing those near-glitches into glitches, that can be fun. But that, in addition to the hit cancellations just seems to be overly punishing. It won't affect good rolls, but it will make mediocre rolls worse, and poor rolls flat-out bad. And it definitely increases the percentage of glitches that are going to be critical glitches, even if they would have formerly succeeded...