Updating a Leaderstat value in a Gui via RemoteEvent?

Hello!

I have a Custom PlayerList, which displays a user's avatar, name, kills for that round, and a killstreak. So far, all the things work. Slight problem - the round kills/killstreak display only updates when the player dies/respawns, instead of as it happens.

There is a RemoteEvent inside ReplicatedStorage labeled as KillUpdate

Here's the LocalScript inside the ScreenGui under StarterGui for the Custom Player List:

game.StarterGui:SetCoreGuiEnabled("PlayerList", false)
local plr = game.Players.LocalPlayer
local kills = plr.leaderstats.Roundkills.Value
local killstreak = plr.leaderstats.Killstreak.Value
local Avatarurl = "http://www.roblox.com/Thumbs/Avatar.ashx?x=500&y=500&Format=Png&username="

while wait(1) do

    for _,plr in pairs (game.Players:GetChildren()) do
        if script.Parent.Holder:FindFirstChild(plr.Name) then

        else
            local kills2 = plr.leaderstats.Roundkills.Value
            local killstreak2 = plr.leaderstats.Killstreak.Value
            I = Instance.new("Frame")
            I.Name = plr.Name
            I.Parent = script.Parent.Holder
            I.Style = "DropShadow"
-- NAME        
            T = Instance.new("TextLabel")
        T.Name = "Username"
            T.BackgroundTransparency = 1
            T.Text = plr.Name
            T.Parent = I
            T.Size = UDim2.new(0, 165, 0, 35)
            T.Position = UDim2.new(0, 10, 0, 0)
            if plr.Name == game.Players.LocalPlayer.Name then
                T.TextColor3 = Color3.fromRGB(0, 200, 255)
                else
            T.TextColor3 = Color3.new(1, 1, 1)
            end
            T.TextStrokeColor3 = Color3.new(0, 0, 0)
            T.TextStrokeTransparency = 0.5
            T.TextXAlignment = "Left"
            T.Font = "SourceSansBold"
            T.TextSize = 20
-- KILLS           
            K = Instance.new("TextLabel")
            K.Name = "RoundKills"
            K.BackgroundTransparency = 1
            K.Text = kills2     
            K.Parent = I
            K.Size = UDim2.new(0, 20, 0, 35)
            K.Position = UDim2.new(0, 155, 0, 0)
            K.TextColor3 = Color3.new(1, 1, 1)
                K.TextStrokeColor3 =  Color3.new(0, 0, 0)
                K.TextStrokeTransparency = 0.5
                K.TextXAlignment = "Right"
                K.Font = "SourceSansBold"
                K.TextSize = 20


-- KILL STREAK Stuff

-- AVATAR IMAGE Stuff


-- REMOTE EVENT CALL:

local event = game:GetService("ReplicatedStorage"):WaitForChild("KillUpdate")
K.Changed:connect(function()
    local amountOfKills = K.Text
    event:FireServer(amountOfKills)
print("Test1")


end)
end
end
end

Script inside ServerScriptStorage:

local event = game:GetService("ReplicatedStorage"):WaitForChild("KillUpdate")
event.OnServerEvent:connect(function(player,amountOfKills)
    player.leaderstats.Roundkills.Value = amountOfKills
end)