For me I think I would replace the Elite Riot Gear with some light weight recon armor, I would possibly keep an AMR on me but it certainly wouldnt be my primary weapon( far far too loud), I would have something like the Gobi Campaign or Christines COS rifle.
RThen I would have a silenced .45 pistol( for sneaking into casinos ant what not) and this may sound out od place but I would most certainly keep a Riot shotty on me. Yea yea yea I know its not a traditional weapon for a sniper, but the riot shotty can save your life is someone manages to sneak up on ya and all you have are weapons best suited for long/ medium range.
thats alot of weapons and ammo and weight. Recon armor isnt too light either, isnt it 25 weight units? For RP purposes Im keep trying to limit myself to a small melee weapon, a sidearm and a longarm so for example using the Cowboy perk all Id need would be a Hatchet, a .44 pistol and a scoped Trail Carbine and maybe some dynamite thus really cutting down on my weight not only by total weapons carried but by sharing ammo types too. It worked better on paper though since the trail carbine isnt suppressed so I couldnt be a sniper and without Hand Loader and/or a high repair skill I couldnt really make anything like AP ammo for the TC either. The search continues but it bears mentioning
as to the OP I still recommend combining the two roles of the AMR and Hunting Rifle into just the Sniper rifle, though I can understand the BAMF factor for the AMR so as an alternative you may want to keep it and just have something like a marksman carbine (or All American) and That Gun as a bread and butter weapon and sidearm, respectively that share ammo types to boot! The only snag I see could be if That Gun isnt considered an improved holdout weapon. Is it?
Long-range or hard targets: AMR
Medium range or moderate targets: Marksman Carbine/All-American
Sidearm and soft targets: That Gun
Ammo needed: 50 cal and 556 and additional explosives and a small melee weapon.