^ Ah.
That is reading like it is mostly a software issue, and not necessarily a hardware issue.
If you're gripping low enough or loose enough that you're not getting the grip safety to properly deactivate, you're going to have bigger problems than the dead trigger on the draw. If your grip is that compromised, it's more than possible that you're going to induce a stoppage once that first shot goes out (i.e. that the end-result would be akin to "limp wristing") or that in a close-quarters/entangled scenario, that gun will be all too easy to wrestle from your hand. In either case, even with a handgun that doesn't have the grip safety as a worry, you're still going to be fighting from way low on the power curve.
The key to a good draw from concealment is efficiency and consistency. The efficiency translates directly into speed. The consistency translates into a solid fighting platform.
In order to achieve this, it means that EACH and EVERY draw you practice needs to be an absolutely perfect repetition. You can be super-diligent and do 1,000 reps of the draw a day, but if each rep is rushed and imperfect, that's going to be a thousand different variations that you're putting into your brain. Instead, slowing down and doing just 20 absolutely perfect draws and presentations, ending each with a perfect dry-fire press as that sight package settles in, will ingrain what that path SHOULD be, so that even under dire stress, you'll still get it perfect.
* not my video
^ Pat McNamara there is on an OWB setup, but the idea is the same. Those sub-2 second draws looked like an eternity on each rep, right?
He's about 10 years older than I am, too, in his low-mid-50s now, IIRC - and he's professed that his eyesight is making it difficult for him to get a sharp front sight on the sight package. But you know what, I'll bet dollars to balls that those shots of his, at that speed, are literally laying right on top of each other, cloverleaf.
Draw-to-first-shot is not about a spastic "rip and grip."

That seeming speed is actually just the manifestation of the efficiency of what is an absolutely regimented and perfected set of movements.
The master grip is everything. It's got to be established before that gun comes out of the holster. Whether you're competing or shooting dynamically for a "tactical" class or entangled in a force-on-force fight with two guys who are both twice your size, you can't afford to be playing with that grip after the gun comes out of the holster - you'll be slower to the shot or compromise recoil-control (thus leading to slower follow-up shots) at-best...at worst, you're going to be inducing a stoppage after that first shot or you're going to lose that gun because someone manages to rip it from your hand or that it just drops free from an otherwise really not that bad of a bump/fall.
If your master-grip is imperfect, you've got to slow down and ask yourself where is it flying apart. Is it because of how you've set your holster to present the gun? Or is it because your draw stroke is inconsistent at that point?
Your Vedder Lite Tuck thread shows the following picture:
http://www.xdtalk.com/posts/6570857/
That is a known-quantity holster, and it looks like there should be more than enough grip above the belt/waist-line for you to grab and achieve a good grip.
I do see that the clip is set to a significant cant, though - does this correspond well with the natural break-over angle at your wrist, when you draw from whatever clocking you currently have the holster sitting? This can potentially make for that initial mis-grab.
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All that said, you noted:
I'm high enough up, but there's enough gap between the web of my hand and the grip to not sufficiently depress the safety.
If the web between your thumb and trigger finger is at the tang/beavertail, then the only possible incorrect execution that would cause the grip safety to not be sufficiently depressed would be a severe undergrip, like what's seen on the LEFT panel, below:
* stolen from ( Grip Your Handgun Correctly and Shoot Better | Colorado Concealed Carry )
With that undergrip, I can get to the point where my palm opens up enough that I sometimes get a dead trigger - but with my hand/finger size (I'm a "large," as measured via both Magpul's glove selection as well as the SKD PIG glove line-up, whose "large" size fits on me like a second skin; I squeeze into size 7 ad 1/2 surgical gloves, though, because I like that fit to be really, really tight, so YMMV :lol: ), I find that I can barely trip the trigger safety sufficiently.
With an overgrip, as typified by the RIGHT most panel above, my thumb actually holds down the trigger safety.
If a severe undergrip is your problem, that's something you need to fix on the software side. Physically altering the grip is also possible, but it should be for final/fine fitting, not to correct for a problem in technique.
It's also possible that if your hand lacks a really prominent thenar eminance, you may not be able to depress the grip safety sufficiently. In this case, the extended grip safeties should be a viable fix.
But if we roll back to the holster setup question before the break, above, it's possible that too-severe of a cant on the holster setup can cause your wrist to not be able to break over far enough to sufficiently bed the web of your dominant hand into the beavertail/tang of the grip, and thus cause a void in that area, despite the appearance that you're actually gripping high enough. To achieve sufficient control over the gun, you've really got to get that web crammed into the beavertail/tang area:
* again, not my video
Just look at the beginning minute and 30 seconds, for now.
Here, you'll note that Vogel's grip is so high that he actually has some scars from where the slide's bitten him in the past. With the way the XD-platform double-stackers are built, it's going to be virtually impossible to ride your hand that high, but you should have your hand literally as far up into that beavertail/tang as possible.
Would it be possible for you to post pictures or videos of your problem?
Also, out of curiosity, where are you in Ohio? I may have asked you this before, but it managed to slip my mind.
Ohio is one of those weird states where there's good training resources pretty much all-over. 