They are pricey, but I use one of these.
Real use gear for backcountry travelers
hillpeoplegear.com
Really??? Barmcd (the OP) is talking about a 7-day, 90-mile backpacking trip. There's no way in heck I can see one of those Hill People chest packs (and I HAVE looked at a few of them) working under of a full-sized backpack with shoulder straps and a chest harness like the OP said his backpack has.
In our younger years, my wife and I backpacked literally hundreds of miles in the Idaho and Wyoming wildernesses. And I myself spent a week on Rainier and 23 days on Denali wearing a full-sized backpack. I wasn't wearing a gun on Rainier or Denali, but I
was on every other backpacking trip I was ever on, and how & where to carry a gun while wearing a 6,000+ cubic- inch backpack was always a problem. I usually ended up
open carrying it by making room on my waistbelt - sort of an open "appendix carry."
However, I eventually found a chest pouch that attached between my backpack's shoulder straps, and I used that for a while. The problems with it were that it was slow to get into, and awkward as all get out when I took my backpack off because I had to unfasten the chest pouch from one shoulder strap or the other. Besides, it didn't hold my relatively heavy revolver close to my chest. And of course, my revolver was in the pouch on my backpack while we were in camp - not the best situation to be in if a bear would have ever come into camp.
BTW - I now believe that carrying a full-sized, heavy revolver as a backpacking gun was silly anyway. I carried a heavy revolver (either a 44 Mag of Ruger 45 Colt) for "bear protection" of course. And in all of my wife's and my backpacking years, the only grizzlies we ever saw were in national parks (where if you shoot a grizzly, you'd better be wearing claw marks) and the only blackbears we ever saw were running away.
So, I now believe I'd have been a lot better off carrying my Glock 19 on our backpacking trips - because the times when I felt the most ill-at-ease on our backpacking trips were when we were at trailheads. Miscreants and other two-legged predators sometimes hang out at trailheads. Yet we never saw those types once we got a mile into the wilderness.
We even considered buying a "backpacking vehicle" (a beat-up old pickup or station wagon) because we were always afraid that when we got back to the trailhead after spending 4 or 5 days (or a week) 30 miles into a wilderness somewhere, we'd find our late-model car or pickup had been broken into. It never happened, but we worried about it.
One more thing before I close - there's a "sticky" (I think that's what it's called) about What Gun for Bears. And I've never clicked on it. But I'd bet there are many posts in it recommending shotguns for bear-protection. Shotguns are fine for bear-protection AFAIC, but anyone who thinks carrying a shotgun for bear-protection while backpacking has never done any
real backpacking. And a shotgun would make a
lousy hiking staff.